networks of theta neurons with time varying excitability macroscopic chaos multistability and final state uncertainty abstract using recently developed analytical techniques we study the macroscopic dynamics of a large heterogeneous network of theta neurons in which the neurons excitability parameter varies in time we demonstrate that such periodic variation can lead to the emergence of macroscopic chaos multistability and final state uncertainty in the collective behavior of the network finite size network effects and rudimentary control via an accessible macroscopic network parameter is also investigated

variable delay feedback control of unstable steady states in retarded time delayed systems we study the stability of unstable steady states in scalar retarded time delayed systems subjected to a variable delay feedback control the important aspect of such a control problem is that time delayed systems are already infinite dimensional before the delayed feedback control is turned on when the frequency of the modulation is large compared to the system s dynamics the analytic approach consists of relating the stability properties of the resulting variable delay system with those of an analogous distributed delay system otherwise the stability domains are obtained by a numerical integration of the linearized variable delay system the analysis shows that the control domains are significantly larger than those in the usual time delayed feedback control and that the complexity of the domain structure depends on the form and the frequency of the delay modulation

delayed feedback control of periodic orbits without torsion in nonautonomous chaotic systems theory and experiment we demonstrate theoretically and experimentally that the unstable delayed feedback controller is an efficient tool for stabilizing torsion free unstable periodic orbits in nonautonomous chaotic systems to improve the global control performance we introduce a two step control algorithm the problem of a linear stability of the system under delayed feedback control is treated analytically theoretical results are confirmed by electronic circuit experiments for a forced double well oscillator

a hybrid asymptotic numerical method for low reynolds number flows past a cylindrical body the classical problem of slow steady two dimensional flow of a viscous incompressible fluid around an infinitely long straight cylinder is considered the cylinder cross section is symmetric about the direction of the oncoming stream but otherwise is arbitrary for low reynolds number the well known singular perturbation analysis for this problem shows that the asymptotic expansions of the drag coefficient and of the flow field start with infinite logarithmic series we show that the entire infinite logarithmic expansions of the flow field and of the drag coefficient are contained in the solution to a certain related problem that does not involve the cross sectional shape of the cylinder the solution to this related problem is computed numerically using a straightforward finite difference scheme the drag coefficient for a cylinder of a specific cross sectional shape which is asymptotically correct to within all logarithmic terms is given in terms of a single shape dependent constant that is determi

variability in noise driven integrator neurons neural variability in the presence of noise has been studied mainly in resonator neurons such as hodgkinhuxley or fitzhugh nagumo models here we investigate this variability for integrator neurons whose excitability is due to a saddle node bifurcation of the rest state instead of a hopf bifurcation using simple theoretical expressions for the interspike times distributions we obtain coefficients of variation in good agreement with numerical calculations in realistic neuron models the main features of this coefficient as a function of noise depend on the refractory period and on the presence of bistability the bistability is responsible for the existence of two different time scales in the spiking behavior giving an antiresonance effect

delay stabilization of rotating waves near fold bifurcation and application to all optical control of a semiconductor laser we consider the delayed feedback control method for stabilization of unstable rotating waves near a fold bifurcation theoretical analysis of a generic model and numerical bifurcation analysis of the rate equations model demonstrate that such orbits can always be stabilized by a proper choice of control parameters our paper confirms the recently discovered invalidity of the so called odd number limitation of delayed feedback control previous results have been restricted to the vicinity of a subcritical hopf bifurcation we now refute such a limitation for rotating waves near a fold bifurcation we include an application to all optical realization of the control in three section semiconductor lasers

a comparison of numerical algorithms for fourier extension of the first second and third kinds the range of fourier methods can be significantly increased by extending a nonperiodic function f x to a periodic function f on a larger interval when f x is analytically known on the extended interval the extension is straightforward when f x is unknown outside the physical interval there is no standard recipe worse still like a radarless aircraft groping through fog the algorithm may wreck on the mountain in fog problem a function f x which is perfectly well behaved on the physical interval may very well have singularities in the extended domain in this article we compare several algorithms for successfully extending a function f x into the fog even when the analytic extension is singular the best third kind extension requires singular value decomposition with iterative refinement but achieves accuracy close to machine precision

delay can stabilize love affairs dynamics abstract we discuss two models of interpersonal interactions with delay the first model is linear and allows the presentation of a rigorous mathematical analysis of stability while the second is nonlinear and a typical local stability analysis is thus performed the linear model is a direct extension of the classic strogatz model on the other hand as interpersonal relations are nonlinear dynamical processes the nonlinear model should better reflect real interactions both models involve immediate reaction on partner s state and a correction of the reaction after some time the models we discuss belong to the class of two variable systems with one delay for which appropriate delay stabilizes an unstable steady state we formulate a theorem and prove that stabilization takes place in our case we conclude that considerable meaning large enough but not too large values of time delay involved in the model can stabilize love affairs dynamics

analytical properties and optimization of time delayed feedback control time delayed feedback control is an efficient method for stabilizing unstable periodic orbits of chaotic systems if the equations governing the system dynamics are known the success of the method can be predicted by a linear stability analysis of the desired orbit unfortunately the usual procedures for evaluating the floquet exponents of such systems are rather intricate we show that the main stability properties of the system controlled by time delayed feedback can be simply derived from a leading floquet exponent defining the system behavior under proportional feedback control optimal parameters of the delayed feedback controller can be evaluated without an explicit integration of delay differential equations the method is valid for low dimensional systems whose unstable periodic orbits are originated from a period doubling bifurcation and is demonstrated for the rossler system and the duffing oscillator

nonlinear coupling near a degenerate hopf bautin bifurcation a nonlinearly coupled system of bistable fixed point and limit cycle differential equations is analyzed the nonlinear equations arise from the first several terms in the normal form expansion near a bautin bifurcation existence and stability of in phase and out of phase periodic solutions to a pair of identical systems are explored existence uniqueness and stability of traveling wave solutions from a stable rest state to a stable periodic solution are proved for the associated evolution convolution equation numerical simulations suggest some interesting patterns in regimes where waves no longer exist the results are shown to hold for a nonreduced conductance based model

improving the precision of noisy oscillators abstract we consider how the period of an oscillator is affected by white noise with special attention given to the cases of additive noise and parameter fluctuations our treatment is based upon the concepts of isochrons which extend the notion of the phase of a stable periodic orbit to the basin of attraction of the periodic orbit and phase response curves which can be used to understand the geometry of isochrons near the periodic orbit this includes a derivation of the leading order effect of noise on the statistics of an oscillator s period several examples are considered in detail which illustrate the use and validity of the theory and demonstrate how to improve a noisy oscillator s precision by appropriately tuning system parameters or operating away from a bifurcation point it is also shown that appropriately timed impulsive kicks can give further improvements to oscillator precision

bifurcation analysis of a class of first order nonlinear delay differential equations with reflectional symmetry abstract we consider a general class of first order nonlinear delay differential equations ddes with reflectional symmetry and study completely the bifurcations of the trivial equilibrium under some generic conditions on the taylor coefficients of the dde our analysis reveals a hopf bifurcation curve terminating on a pitchfork bifurcation line at a codimension two takens bogdanov point in parameter space we compute the normal form coefficients of the reduced vector field on the centre manifold in terms of the taylor coefficients of the original dde and in contrast to many previous bifurcation analyses of ddes we also compute the unfolding parameters in terms of these coefficients for application purposes this is important since one can now identify the possible asymptotic dynamics of the dde near the bifurcation points by computing quantities which depend explicitly on the taylor coefficients of the original dde we illustrate these results using simple model systems relevant to the areas of neural networks and atmospheric physics and show that the results agree with numerical simulations

pyragas stabilizability via delayed feedback with periodic control gain abstract in this paper for the unstable periodic solution of nonlinear differential equation pyragas stabilizability problem is studied an algorithm of stabilization via periodical delayed feedback is obtained the consideration is based on the theory of nonstationary stabilization

on the degree distribution of projected networks mapped from bipartite networks abstract many real world systems can be represented by bipartite networks in a bipartite network the nodes are divided into two disjoint sets and the edges connect nodes that belong to different sets given a bipartite network i e two mode network it is possible to construct two projected networks i e one mode networks where each one is composed of only one set of nodes while network analyses have focused on unipartite networks considerably less attention has been paid to the analytical study of bipartite networks here we analytically derive simple mathematical relationships that predict degree distributions of the projected networks by only knowing the structure of the original bipartite network these analytical results are confirmed by computational simulations using artificial and real world bipartite networks from a variety of biological and social systems these findings offer in our view new insights into the structure of real world bipartite networks

control and synchronization of neuron ensembles synchronization of oscillations is a phenomenon prevalent in natural social and engineering systems controlling synchronization of oscillating systems is motivated by a wide range of applications from surgical treatment of neurological diseases to the design of neurocomputers in this paper we study the control of an ensemble of uncoupled neuron oscillators described by phase models we examine controllability of such a neuron ensemble for various phase models and furthermore study the related optimal control problems in particular by employing pontryagin s maximum principle we analytically derive optimal controls for spiking single and two neuron systems and analyze the applicability of the latter to an ensemble system finally we present a robust computational method for optimal control of spiking neurons based on pseudospectral approximations the methodology developed here is universal to the control of general nonlinear phase oscillators

control of unstable steady states by long delay feedback we present an asymptotic analysis of time delayed feedback control of steady states for large delay time by scaling arguments and a detailed comparison with exact solutions we establish the parameter ranges for successful stabilization of an unstable fixed point of focus type insight into the control mechanism is gained by analyzing the eigenvalue spectrum which consists of a pseudocontinuous spectrum and up to two strongly unstable eigenvalues although the standard control scheme generally fails for large delay we find that if the uncontrolled system is sufficiently close to its instability threshold control does work even for relatively large delay times

spectral integration of linear boundary value problems spectral integration was deployed by orszag and co workers 1977 1980 1981 to obtain stable and efficient solvers for the incompressible navier stokes equation in rectangular geometries since then several variations of spectral integration have appeared in the literature in this article we derive yet more versions of spectral integration these new versions of spectral integration rely exclusively on banded matrices as opposed to banded matrices bordered with dense rows in addition we derive a factored form of spectral integration which relies only on bi and tri diagonal matrices key properties such as the accuracy of spectral integration even when green s functions are not resolved by the underlying grid and the accuracy of spectral integration in spite of ill conditioning of underlying linear systems are investigated timed comparisons show that reducing spectral integration to bi and tri diagonal systems leads to significant speed ups

type i membranes phase resetting curves and synchrony type i membrane oscillators such as the connor model connor et al 1977 and the morris lecar model morris and lecar 1981 admit very low frequency oscillations near the critical applied current hansel et al 1995 have numerically shown that synchrony is difficult to achieve with these models and that the phase resetting curve is strictly positive we use singular perturbation methods and averaging to show that this is a general property of type i membrane models we show in a limited sense that so called type ii resetting occurs with models that obtain rhythmicity via a hopf bifurcation we also show the differences between synapses that act rapidly and those that act slowly and derive a canonical form for the phase interactions

towards easier realization of time delayed feedback control of odd number orbits we develop generalized time delayed feedback schemes for the stabilization of periodic orbits with an odd number of positive floquet exponents which are particularly well suited for experimental realization we construct the parameter regimes of successful control and validate these by numerical simulations and numerical continuation methods in particular it is shown how periodic orbits can be stabilized with symmetric feedback matrices by introducing an additional latency time in the control loop finally we show using normal form analysis and numerical simulations how our results could be implemented in a laser setup using optoelectronic feedback

delayed feedback control of the lorenz system an analytical treatment at a subcritical hopf bifurcation we develop an analytical approach for the delayed feedback control of the lorenz system close to a subcritical hopf bifurcation the periodic orbits arising at this bifurcation have no torsion and cannot be stabilized by a conventional delayed feedback control technique we utilize a modification based on an unstable delayed feedback controller the analytical approach employs the center manifold theory and the near identity transformation we derive the characteristic equation for the floquet exponents of the controlled orbit in an analytical form and obtain simple expressions for the threshold of stability as well as for an optimal value of the control gain the analytical results are supported by numerical analysis of the original system of nonlinear differential difference equations

conversion of stability in systems close to a hopf bifurcation by time delayed coupling we propose a control method with time delayed coupling which makes it possible to convert the stability features of systems close to a hopf bifurcation we consider two delay coupled normal forms for hopf bifurcation and demonstrate the conversion of stability i e an interchange between the sub and supercritical hopf bifurcation the control system provides us with an unified method for stabilizing both the unstable periodic orbit and the unstable steady state and reveals typical effects like amplitude death and phase locking the main method and the results are applicable to a wide class of systems showing hopf bifurcations for example the van der pol oscillator the analytical theory is supported by numerical simulations of two delay coupled van der pol oscillators which show good agreement with the theory

experimental verification of pyragas scholl fiedler control we present an experimental realization of time delayed feedback control proposed by scholl and fiedler the scheme enables us to stabilize torsion free periodic orbits in autonomous systems and to overcome the so called odd number limitation the experimental control performance is in quantitative agreement with the bifurcation analysis of simple model systems the results uncover some general features of the control scheme which are deemed to be relevant for a large class of setups

a maple program for computing a terms of a center manifold and element of bifurcations for a class of retarded functional differential equations with hopf singularity in this paper we present explicit formulas for computing the coefficients of a center manifold for the hopf singularity in autonomous retarded functional differential equations as consequence an algorithm for computing lyapunov constant and normal forms up to an arbitrary order is derived the explicit formulas have been implemented using the computer algebra system maple the paper ends with some examples in order to show the applicability of the methodology and the convenience of the computer software

class ii neurons display a higher degree of stochastic synchronization than class i neurons we describe the relationship between the shape of the phase resetting curve prc and the degree of stochastic synchronization observed between a pair of uncoupled general oscillators receiving partially correlated poisson inputs in addition to inputs from independent sources we use perturbation methods to derive an expression relating the shape of the prc to the probability density function pdf of the phase difference between the oscillators we compute various measures of the degree of synchrony and cross correlation from the pdf s and use the same to compare and contrast differently shaped prcs with respect to their ability to undergo stochastic synchronization since the shape of the prc depends on underlying dynamical details of the oscillator system we utilize the results obtained from the analysis of general oscillator systems to study specific models of neuronal oscillators it is shown that the degree of stochastic synchronization is controlled both by the firing rate of the neuron and the membership of the prc type i or type ii it is also shown that the circular variance for the integrate and fire neuron and the generalized order parameter for a hippocampal interneuron model have a nonlinear relationship to the input correlation

beyond the odd number limitation a bifurcation analysis of time delayed feedback control we investigate the normal form of a subcritical hopf bifurcation subjected to time delayed feedback control bifurcation diagrams which cover time dependent states as well are obtained by analytical means the computations show that unstable limit cycles with an odd number of positive floquet exponents can be stabilized by time delayed feedback control contrary to incorrect claims in the literature the model system constitutes one of the few examples where a nonlinear time delay system can be treated entirely by analytical means

on global properties of time delayed feedback control weakly nonlinear analysis we address the problem which type of initial state yields successful stabilisation when time delayed feedback control is applied using well known concepts from bifurcation theory we provide a general mechanism that limits the corresponding basins of attraction application of normal form analysis to general delay differential equations proves the universality of our results the empirical criteria which determine the prospective size of the basin are easily accessible and a demonstration in terms of a simple numerical simulation is provided

time delayed feedback control of unstable periodic orbits near a subcritical hopf bifurcation we show that the pyragas delayed feedback control can stabilize an unstable periodic orbit upo that arises from a generic subcritical hopf bifurcation of a stable equilibrium in an n dimensional dynamical system this extends results of fiedler et al b fiedler v flunkert m georgi p hovel e scholl refuting the odd number limitation of time delayed feedback control phys rev lett 98 11 2007 114101 who demonstrated that such a feedback control can stabilize the upo associated with a two dimensional subcritical hopf normal form the pyragas feedback requires an appropriate choice of a feedback gain matrix for stabilization as well as knowledge of the period of the targeted upo we apply feedback in the directions tangent to the two dimensional center manifold we parameterize the feedback gain by a modulus and a phase angle and give explicit formulae for choosing these two parameters given the period of the upo in a neighborhood of the bifurcation point we show first heuristically and then rigorously by a center manifold reduction for delay differential equations that the stabilization mechanism involves a highly degenerate hopf bifurcation problem that is induced by the time delayed feedback when the feedback gain modulus reaches a threshold for stabilization both of the genericity assumptions associated with a two dimensional hopf bifurcation are violated the eigenvalues of the linearized problem do not cross the imaginary axis as the bifurcation parameter is varied and the real part of the cubic coefficient of the normal form vanishes our analysis reveals two qualitatively distinct cases when the degenerate bifurcation is unfolded in a two parameter plane in each case the pyragas type feedback successfully stabilizes the branch of small amplitude upos in a neighborhood of the original bifurcation point provided that the feedback phase angle satisfies a certain restriction

identification and continuity of the distributions of burst length and interspike intervals in the stochastic morris lecar neuron using the morris lecar model neuron with a type ii parameter set and k channel noise we investigate the interspike interval distribution as increasing levels of applied current drive the model through a subcritical hopf bifurcation our goal is to provide a quantitative description of the distributions associated with spiking as a function of applied current the model generates bursty spiking behavior with sequences of random numbers of spikes bursts separated by interburst intervals of random length this kind of spiking behavior is found in many places in the nervous system most notably perhaps in stuttering inhibitory interneurons in cortex here we show several practical and inviting aspects of this model combining analysis of the stochastic dynamics of the model with estimation based on simulations we show that the parameter of the exponential tail of the interspike interval distribution is in fact continuous over the entire range of plausible applied current regardless of the bifurcations in the phase portrait of the model further we show that the spike sequence length apparently studied for the first time here has a geometric distribution whose associated parameter is continuous as a function of applied current over the entire input range hence this model is applicable over a much wider range of applied current than has been thought

non resonant double hopf bifurcation of a class b laser system we investigate the double hopf bifurcation at positive equilibrium point of a class b laser system firstly we give the critical values of hopf and double hopf bifurcations secondly we implement the normal form method and the center manifold theory for a class b laser system and derive the universal unfolding of the double hopf bifurcation thirdly some dynamic behaviors such as periodic and quasi periodic solutions are observed using numerical simulation

fourier embedded domain methods extending a function defined on an irregular region to a rectangle so that the extension is spatially periodic and c a simple way to solve a partial differential equation in a non rectangular domain w is to embed the domain in a rectangle b and solve the problem more easily in the rectangle to apply a fourier spectral method on the rectangle it is necessary to extend the inhomogeneous term in the pde f x y to b in such a way that the extended function g x y is periodic and infinitely differentiable and yet is equal to f x y everywhere in the irregular domain w if the boundary of w email protected is defined as the zero isoline of a function f x y then a suitable extension is g x y f x y h email protected x y constant where h is a smoothed approximation to the step function which is defined in the main text

time delay autosynchronization of the spatiotemporal dynamics in resonant tunneling diodes the double barrier resonant tunneling diode exhibits complex spatiotemporal patterns including low dimensional chaos when operated in an active external circuit we demonstrate how autosynchronization by time delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way we compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom the numerically obtained floquet exponents are explained by analytical results from linear stability analysis

asynchronous states and the emergence of synchrony in large networks of interacting excitatory and inhibitory neurons we investigate theoretically the conditions for the emergence of synchronous activity in large networks consisting of two populations of extensively connected neurons one excitatory and one inhibitory the neurons are modeled with quadratic integrate and fire dynamics which provide a very good approximation for the subthreshold behavior of a large class of neurons in addition to their synaptic recurrent inputs the neurons receive a tonic external input that varies from neuron to neuron because of its relative simplicity this model can be studied analytically we investigate the stability of the asynchronous state as of the network with given average firing rates of the two populations first we show that the as can remain stable even if the synaptic couplings are strong then we investigate the conditions under which this state can be destabilized we show that this can happen in four generic ways the first is a saddle node bifurcation which leads to another state with different average firing rates this bifurcation which occurs for strong enough recurrent excitation does not correspond to the emergence of synchrony in contrast in the three other instability mechanisms hopf bifurcations which correspond to the emergence of oscillatory synchronous activity occur we show that these mechanisms can be differentiated by the firing patterns they generate and their dependence on the mutual interactions of the inhibitory neurons and cross talk between the two populations we also show that besides these codimension 1 bifurcations the system can display several codimension 2 bifurcations takens bogdanov gavrielov guckenheimer and double hopf bifurcations

normal forms for retarded functional differential equations with parameters and applications to hopf bifurcation abstract the paper addresses for retarded functional differential equations fdes with parameters the computation of normal forms associated with the flow on a finite dimensional invariant manifold tangent to an invariant space for the infinitesimal generator of the linearized equation at a singularity the analysis is based on the theory previously developed for fdes without parameters by considering an extension of a phase space appropriate to the computation of these normal forms as an application the generic hopf bifurcation for scalar retarded fdes is considered

stabilizing unstable periodic orbits in the lorenz equations using time delayed feedback control for many years it was believed that an unstable periodic orbit with an odd number of real floquet multipliers greater than unity cannot be stabilized by the time delayed feedback control mechanism of pyragas a recent paper by fiedler et al phys rev lett 98 114101 2007 uses the normal form of a subcritical hopf bifurcation to give a counterexample to this theorem using the lorenz equations as an example we demonstrate that the stabilization mechanism identified by fiedler et al for the hopf normal form can also apply to unstable periodic orbits created by subcritical hopf bifurcations in higher dimensional dynamical systems our analysis focuses on a particular codimension two bifurcation that captures the stabilization mechanism in the hopf normal form example and we show that the same codimension two bifurcation is present in the lorenz equations with appropriately chosen pyragas type time delayed feedback this example suggests a possible strategy for choosing the feedback gain matrix in pyragas control of unstable periodic orbits that arise from a subcritical hopf bifurcation of a stable equilibrium in particular our choice of feedback gain matrix is informed by the fiedler et al example and it works over a broad range of parameters despite the fact that a center manifold reduction of the higher dimensional problem does not lead to their model problem

some basic remarks on eigenmode expansions of time delay dynamics abstract we describe in elementary terms how eigenmode expansions can be used to deal with differential difference equations as particular applications we present the full analytical solution of linear stochastic time delay systems and the weakly nonlinear analysis of nonlinear differential difference equations in the limit of large time delay our exposition is essentially based on an explicit analytical expression for the linear spectrum in terms of the lambert w function and on the explicit formula for the eigenfunctions of the adjoint equation

the fourier transform of the quartic gaussian exp ax4 hypergeometric functions power series steepest descent asymptotics and hyperasymptotics and extensions to exp ax2n the fourier transform of a quartic gaussian f k exp ikx exp x 4 dx is important in the theory of radial basis functions with f r exp r 4 we show that the transform is the exact sum of two generalized hypergeometric functions 0f 2 this implies that f k is an entire function and also gives an analytical form for the power series coefficients of arbitrary degree using the method of steepest descent for integrals we derive the first five terms in an asymptotic series in powers of k 4 3 through a simple hyperasymptotic analysis we show that the magnitude of the error of the optimally truncated series superasymptotic error is oexp 0 818k 4 3 the lowest order approximation f k 2 7 6 p 3k 1 3exp 2 1 33 16 k 4 3 cos 3 3 22 1 3 16 k 4 3 p 6 shows that the transform f k is an exponentially decaying oscillation we show that the steepest descent method 2 27 bender and orszag 1978 miller 2006 26 33 lauwerier 1966 ursell 1965 can be applied to the transform of exp ax 2 n for general integer n and give the first two terms another theme is that modern computer technology has simplified the steepest descent method the steepest descent paths can be plotted by merely displaying the contours of the imaginary part of the phase function j t where z j t is the logarithm of the integrand and z is the large parameter here proportional to k 4 3 the task of inverting w t to obtain a series in powers of w for the metric factor dt dw after the usual change of integration variable can now be done to high order by a few lines of an algebraic manipulation language as illustrated by a short table with the complete maple code

hyperasymptotics and the linear boundary layer problem why asymptotic series diverge the simplest problem with boundary layers epsilon 2 u xx u f x is used to illustrate i why the perturbation series in powers of epsilon is asymptotic but divergent ii why the optimally truncated expansion is superasymptotic in the sense that that error is proportional to exp mbox constant epsilon and iii how to obtain an improved hyperasymptotic approximation

asymptotics beyond all orders asymptotology and borel summation asymptotics superasymptotics hyperasymptotics m berry the geometric model of crystal growth numerical analysis of the geometric model of crystal growth j m hammersley dendritic crystal growth an experimental assessment of continuum models of dendritic growth j p gollub directional solidification of solids directional growth of dilute mixtures and lamellar eutectics k kassner et al flow in a hele shaw cell viscous displacement in a hele shaw cell s tanveer the rapidly forced pendulum exponentially small estimate for separatrix splittings j scheurle et al ordinary differential equations singular perturbations of solitons y pomeau solitary water waves in the presence of small surface tension solitary waves with ripples beyond all orders j t beale problems in optics potpourri 23 additional articles index

delay and periodicity systems with time delay play an important role in modeling of many physical and biological processes in this paper we describe generic properties of systems with time delay which are related to the appearance and stability of periodic solutions in particular we show that delay systems generically have families of periodic solutions which are reappearing for infinitely many delay times as delay increases the solution families overlap leading to increasing coexistence of multiple stable as well as unstable solutions we also consider stability issue of periodic solutions with large delay by explaining asymptotic properties of the spectrum of characteristic multipliers we show that the spectrum of multipliers can be split into two parts pseudocontinuous and strongly unstable the pseudocontinuous part of the spectrum mediates destabilization of periodic solutions

design of charge balanced time optimal stimuli for spiking neuron oscillators in this letter we investigate the fundamental limits on how the interspike time of a neuron oscillator can be perturbed by the application of a bounded external control input a current stimulus with zero net electric charge accumulation we use phase models to study the dynamics of neurons and derive charge balanced controls that achieve the minimum and maximum interspike times for a given bound on the control amplitude our derivation is valid for any arbitrary shape of the phase response curve and for any value of the given control amplitude bound in addition we characterize the change in the structures of the charge balanced time optimal controls with the allowable control amplitude we demonstrate the applicability of the derived optimal control laws by applying them to mathematically ideal and experimentally observed neuron phase models including the widely studied hodgkin huxley phase model and by verifying them with the corresponding original full state space models this work addresses a fundamental problem in the field of neural control and provides a theoretical investigation to the optimal control of oscillatory systems

odd number theorem optical feedback control at a subcritical hopf bifurcation in a semiconductor laser a subcritical hopf bifurcation is prepared in a multisection semiconductor laser in the free running state hysteresis is absent due to noise induced escape processes the missing branches are recovered by stabilizing them against noise through application of phase sensitive noninvasive delayed optical feedback control the same type of control is successfully used to stabilize the unstable pulsations born in the hopf bifurcation this experimental finding represents an optical counterexample to the so called odd number limitation of delayed feedback control however as a leftover of the limitation the domains of control are extremely small

delayed feedback control of chaos bifurcation analysis we study the effect of time delayed feedback control in the form proposed by pyragas on deterministic chaos in the rossler system we reveal the general bifurcation diagram in the parameter plane of time delay and feedback strength k which allows one to explain the phenomena that have been discovered in some previous works we show that the bifurcation diagram has essentially a multi leaf structure that constitutes multistability the larger the time delay the larger the number of attractors that can coexist in the phase space feedback induces a large variety of regimes non existent in the original system among them tori and chaotic attractors born from them finally we estimate how the parameters of delayed feedback influence the periods of limit cycles in the system

two classes of bipartite networks nested biological and social systems bipartite graphs have received some attention in the study of social networks and of biological mutualistic systems a generalization of a previous model is presented that evolves the topology of the graph in order to optimally account for a given contact preference rule between the two guilds of the network as a result social and biological graphs are classified as belonging to two clearly different classes projected graphs linking the agents of only one guild are obtained from the original bipartite graph the corresponding evolution of its statistical properties is also studied an example of a biological mutualistic network is analyzed in detail and it is found that the model provides a very good fitting of all the main statistical features the model also provides a proper qualitative description of the same features observed in social webs suggesting the possible reasons underlying the difference in the organization of these two kinds of bipartite networks

qualitative changes in phase response curve and synchronization at the saddle node loop bifurcation prominent changes in neuronal dynamics have previously been attributed to a specific switch in onset bifurcation the bogdanov takens bt point this study unveils another relevant and so far underestimated transition point the saddle node loop bifurcation which can be reached by several parameters including capacitance leak conductance and temperature this bifurcation turns out to induce even more drastic changes in synchronization than the bt transition this result arises from a direct effect of the saddle node loop bifurcation on the limit cycle and hence spike dynamics in contrast the bt bifurcation exerts its immediate influence upon the subthreshold dynamics and hence only indirectly relates to spiking we specifically demonstrate that the saddle node loop bifurcation i ubiquitously occurs in planar neuron models with a saddle node on invariant cycle onset bifurcation and ii results in a symmetry breaking of the system s phase response curve the latter entails an increase in synchronization range in pulse coupled oscillators such as neurons the derived bifurcation structure is of interest in any system for which a relaxation limit is admissible such as josephson junctions and chemical oscillators

delayed feedback control of fractional order chaotic systems we study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional order dynamical systems by the time delayed feedback method by performing a linear stability analysis we establish the parameter ranges for successful stabilization of unstable equilibria in the plane parameterized by the feedback gain and the time delay an insight into the control mechanism is gained by analyzing the characteristic equation of the controlled system showing that the control scheme fails to control unstable equilibria having an odd number of positive real eigenvalues we demonstrate that the method can also stabilize unstable periodic orbits for a suitable choice of the feedback gain providing that the time delay is chosen to coincide with the period of the target orbit in addition it is shown numerically that delayed feedback control with a sinusoidally modulated time delay significantly enlarges the stability region of steady states in comparison to the classical time delayed feedback scheme with a constant delay

control of unstable steady states by time delayed feedback methods we show that time delayed feedback methods which have successfully been used to control unstable periodic orbits provide a tool to stabilize unstable steady states we present an analytical investigation of the feedback scheme using the lambert function and discuss effects of both a low pass filter included in the control loop and nonzero latency times associated with the generation and injection of the feedback signal

effects of dendritic load on the firing frequency of oscillating neurons we study the effects of passive dendritic properties on the dynamics of neuronal oscillators we find that the addition of a passive dendrite can sometimes have counterintuitive effects on firing frequency specifically the addition of a hyperpolarized passive dendritic load can either increase decrease or have negligible effects on firing frequency we use the theory of weak coupling to derive phase equations for ball and stick model neurons and two compartment model neurons we then develop a framework for understanding how the addition of passive dendrites modulates the frequency of neuronal oscillators we show that the average value of the neuronal oscillator s phase response curves measures the sensitivity of the neuron s firing rate to the dendritic load including whether the addition of the dendrite causes an increase or decrease in firing frequency we interpret this finding in terms of to the slope of the neuronal oscillator s frequency applied current curve we also show that equivalent results exist for constant and noisy point source input to the dendrite we note that the results are not specific to neurons but are applicable to any oscillator subject to a passive load

measurement of infinitesimal phase response curves from noisy real neurons we sought to measure infinitesimal phase response curves iprcs from rat hippocampal ca1 pyramidal neurons it is difficult to measure iprcs from noisy neurons because of the dilemma that either the linearity or the signal to noise ratio of responses to external perturbations must be sacrificed to overcome this difficulty we used an iprc measurement model formulated as the langevin phase equation lpe to extract iprcs in the bayesian scheme we then simultaneously verified the effectiveness of the measurement model and the reliability of the estimated iprcs by demonstrating that lpes with the estimated iprcs could predict the stochastic behaviors of the same neurons whose iprcs had been measured when they were perturbed by periodic stimulus currents our results suggest that the lpe is an effective model for real oscillating neurons and that many theoretical frameworks based on it may be applicable to real nerve systems

consistent spectral predictors for dynamic causal models of steady state responses dynamic causal modelling dcm for steady state responses ssr is a framework for inferring the mechanisms that underlie observed electrophysiological spectra using biologically plausible generative models of neuronal dynamics in this paper we examine the dynamic repertoires of nonlinear conductance based neural population models and propose a generative model of their power spectra our model comprises an ensemble of interconnected excitatory and inhibitory cells where synaptic currents are mediated by fast glutamatergic and gabaergic receptors and slower voltage gated nmda receptors we explore two formulations of how hidden neuronal states depolarisation and conductances interact through their mean and variance mean field model or through their mean alone neural mass model both rest on a nonlinear fokker planck description of population dynamics which can exhibit bifurcations phase transitions we first characterise these phase transitions numerically by varying critical model parameters we elicit both fixed points and quasiperiodic dynamics that reproduce the spectral characteristics 2 100 hz of real electrophysiological data we then introduce a predictor of spectral activity using centre manifold theory and linear stability analysis this predictor is based on sampling the system s jacobian over the orbits of hidden neuronal states this predictor behaves consistently and smoothly in the region of phase transitions which permits the use of gradient descent methods for model inversion we demonstrate this by inverting generative models dcms of ssrs using simulated data that entails phase transitions

numerical bifurcation analysis of delay differential equations numerical methods for the bifurcation analysis of delay differential equations ddes have only recently received much attention partially because the theory of ddes smoothness boundedness stability of solutions is more complicated and less established than the corresponding theory of ordinary differential equations as a consequence no established software packages exist at present for the bifurcation analysis of ddes we outline existing numerical methods for the computation and stability analysis of steady state solutions and periodic solutions of systems of ddes with several constant delays

summation of asymptotic expansions of multiple valued functions using algebraic approximants application to anharmonic oscillators the divergent rayleigh schrodinger perturbation expansions for energy eigenvalues of cubic quartic sextic and octic oscillators are summed using algebraic approximants these approximants are generalized pade approximants that are obtained from an algebraic equation of arbitrary degree numerical results indicate that given enough terms in the asymptotic expansion the rate of convergence of the diagonal staircase approximant sequence increases with the degree different branches of the approximants converge to different branches of the function the success of the high degree approximants is attributed to their ability to model the function on multiple sheets of the riemann surface and to reproduce the correct singularity structure in the limit of large perturbation parameter an efficient recursive algorithm for computing the diagonal approximant sequence is presented

locating unstable periodic orbits when adaptation integrates into delayed feedback control finding unstable periodic orbits upos is always a challenging demand in biophysics and computational biology which needs efficient algorithms to meet this need an approach to locating unstable periodic orbits in chaotic dynamical system is presented the uniqueness of the approach lies in the introduction of adaptive rules for both feedback gain and time delay in the system without requiring any information of the targeted upo periods a priori this approach is theoretically validated under some mild conditions and successfully tested with some practical strategies in several typical chaotic systems with or without significant time delays

global view on a nonlinear oscillator subject to time delayed feedback control we apply time delayed feedback control to stabilise unstable periodic orbits of an amplitude phase oscillator the control acts on both the amplitude and the frequency of the oscillator and we show how the phase of the control signal influences the dynamics of the oscillator a comprehensive bifurcation analysis in terms of the control phase and the control strength reveals large stability regions of the target periodic orbit as well as an increasing number of unstable periodic orbits caused by the time delay of the feedback loop our results provide insight into the global features of time delayed control schemes

optimal entrainment with smooth pulse and square signals in weakly forced nonlinear oscillators abstract a physical limit of entrainability of nonlinear oscillators is considered for an external weak signal forcing this limit of entrainability is characterized by the optimization problem maximizing the width of the arnold tongue the frequency locking range versus forcing magnitude under certain practical constraints here we show a solution to this optimization problem thanks to a direct link to holder s inequality this solution defines an ideal forcing realizing the entrainment limit and as the result a fundamental limit of entrainment is clarified as follows for 1 1 entrainment we obtain i a construction of the global optimal forcing and a condition for its uniqueness in l p space with p 1 and ii a construction of the global optimal pulse like forcings in l 1 space and for m n entrainment m n some informations about the non existence of the ideal forcing iii in addition we establish definite algorithms for obtaining the global optimal forcings for 1 p and these pulse like forcings for p 1 these theoretical findings are verified by systematic extensive numerical calculations and simulations

systematic experimental exploration of bifurcations with noninvasive control we present a general method for systematically investigating the dynamics and bifurcations of a physical nonlinear experiment in particular we show how the odd number limitation inherent in popular noninvasive control schemes such as pyragas time delayed or washout filtered feedback control can be overcome for tracking equilibria or forced periodic orbits in experiments to demonstrate the use of our noninvasive control we trace out experimentally the resonance surface of a periodically forced mechanical nonlinear oscillator near the onset of instability around two saddle node bifurcations folds and a cusp bifurcation

feedback control of flow alignment in sheared liquid crystals based on a continuum theory we investigate the manipulation of the nonequilibrium behavior of a sheared liquid crystal via closed loop feedback control our goal is to stabilize a specific dynamical state that is the stationary flow alignment under conditions where the uncontrolled system displays oscillatory director dynamics with in plane symmetry to this end we employ time delayed feedback control tdfc where the equation of motion for the i th component q i t of the order parameter tensor is supplemented by a control term involving the difference q i t ensuremath q i t ensuremath ensuremath tau in this diagonal scheme ensuremath tau is the delay time we demonstrate that the tdfc method successfully stabilizes flow alignment for suitable values of the control strength k and ensuremath tau these values are determined by solving an exact eigenvalue equation moreover our results show that only small values of k are needed when the system is sheared from an isotropic equilibrium state contrary to the case where the equilibrium state is nematic

stabilization of a steady state in network oscillators by using diffusive connections with two long time delays the present study shows that diffusive connections with two long time delays can induce the stabilization of a steady state in network oscillators a linear stability analysis shows that if the two delay times retain a proportional relation with a certain bias the stabilization can be achieved independent of the delay times furthermore a simple systematic procedure for designing the coupling strength and the delay times in the connections is proposed the procedure has the following two advantages one can employ time delays as long as one wants and the stabilization can be achieved independently of its network topology our analytical results are applied to the well known double scroll circuit model on a small world network

synchronization in networks of excitatory and inhibitory neurons with sparse random connectivity in model networks of e cells and i cells excitatory and inhibitory neurons respectively synchronous rhythmic spiking often comes about from the interplay between the two cell groups the e cells synchronize the i cells and vice versa under ideal conditions homogeneity in relevant network parameters and all to all connectivity for instance this mechanism can yield perfect synchronization we find that approximate imperfect synchronization is possible even with very sparse random connectivity the crucial quantity is the expected number of inputs per cell as long as it is large enough more precisely as long as the variance of the total number of synaptic inputs per cell is small enough tight synchronization is possible the desynchronizing effect of random connectivity can be reduced by strengthening the e i synapses more surprising it cannot be reduced by strengthening the i e synapses however the decay time constant of inhibition plays an important role faster decay yields tighter synchrony in particular in models in which the inhibitory synapses are assumed to be instantaneous the effects of sparse random connectivity cannot be seen

increasing inhibitory input increases neuronal firing rate why and when diffusion process cases increasing inhibitory input to single neuronal models such as the fitzhugh nagumo model and the hodgkin huxley model can sometimes increase their firing rates a phenomenon which we term inhibition boosted firing ibf here we consider neuronal models with diffusion approximation inputs i e they share the identical first and second order statistics of the corresponding poisson process inputs using the integrate and fire model and the if fhn model we explore theoretically how and when ibf can happen for both models it is shown that there is a critical input frequency at which the efferent firing rate is identical when the neuron receives purely excitatory inputs or exactly balanced inhibitory and excitatory inputs when the input frequency is lower than the critical frequency ibf occurs

generalization of coupled spiking models and effects of the width of an action potential on synchronization phenomena the integrate and fire if neuron model and the piecewise linear version of fitzhugh nagumo pl neuron model with a time scale parameter mu are frequently being used in the study of synchronization phenomena although the two models are regarded to be different type we show a certain equivalence between them by deriving the coupled if model of an improved version with a firing duration from the recovery variable coupled system of the pl model under taking the limit of mu 0 without a loss of any coupling properties in the coupled if model with the duration time the synchronization behavior of a pair of neurons with excitatory or inhibitory synaptic coupling can be systematically explored in terms of three parameters in the model synaptic strength decaying relaxation rate of the synaptic coupling and the parameter exhibiting the firing duration we find some irregularly synchronous behavior with or without constant firing order alternations we show that the duration of an impulse plays an important role in synchronization phenomena

delayed feedback control of dynamical systems at a subcritical hopf bifurcation we consider the delayed feedback control of a torsion free unstable periodic orbit originated in a dynamical system at a subcritical hopf bifurcation close to the bifurcation point the problem is treated analytically using the method of averaging we discuss the necessity of employing an unstable degree of freedom in the feedback loop as well as a nonlinear coupling between the controlled system and controller to demonstrate our analytical approach the specific example of a nonlinear electronic circuit is taken as a model of a subcritical hopf bifurcation

phase reduction of weakly perturbed limit cycle oscillations in time delay systems abstract the phase reduction method is applied to a general class of weakly perturbed time delay systems exhibiting periodic oscillations the adjoint equation with an appropriate initial condition for the infinitesimal phase response curve of a time delay system is derived the method is demonstrated numerically for the mackey glass equation as well as for a chaotic rossler system subject to a delayed feedback control dfc we show that the profile of the phase response curve of a periodic orbit stabilized by the dfc algorithm does not depend on the control matrix this property is universal and holds for any dynamical system subject to the dfc

comparison of time delayed feedback schemes for spatiotemporal control of chaos in a reaction diffusion system with global coupling time delayed feedback control for stabilizing time periodic spatial patterns is investigated in a generic reaction diffusion system with global coupling we focus on the case of low dimensional chaos where unstable patterns admit only a single unstable mode spatial degrees of freedom are taken into account to define different control schemes the efficiency of these schemes is discussed where control forces are motivated by physical requirements as well as by the possibility of obtaining analytically exact results we find that control schemes that contain the full feedback of the inhibitor variable may finally destroy the control performance thus schemes that omit the inhibitor might be more efficient our numerical findings are explained in terms of floquet spectra and compared with analytical solutions of particular coupling schemes

phase reduction theory based treatment of extended delayed feedback control algorithm in the presence of a small time delay mismatch the delayed feedback control dfc methods are noninvasive which means that the control signal vanishes if the delay time is adjusted to be equal to the period of a target unstable periodic orbit upo if the delay time differs slightly from the upo period a nonvanishing periodic control signal is observed we derive an analytical expression for this period for a general class of multiple input multiple output systems controlled by an extended dfc algorithm our approach is based on the phase reduction theory adapted to systems with time delay the analytical results are supported by numerical simulations of the controlled rossler system

spatial and temporal feedback control of traveling wave solutions of the two dimensional complex ginzburg landau equation previous work has shown that benjamin feir unstable traveling waves of the complex ginzburg landau equation cgle in two spatial dimensions cannot be stabilized using a particular time delayed feedback control mechanism known as time delay autosynchronization in this paper we show that the addition of similar spatial feedback terms can be used to stabilize such waves this type of feedback is a generalization of the time delay method of pyragas k pyragas continuous control of chaos by self controlling feedback phys lett a 170 1992 421 428 and has been previously used to stabilize waves in the one dimensional cgle by montgomery and silber k montgomery m silber feedback control of traveling wave solutions of the complex ginzburg landau equation nonlinearity 17 6 2004 2225 2248 we consider two cases in which the feedback contains either one or two spatial terms we focus on how the spatial terms may be chosen to select the direction of travel of the plane waves numerical linear stability calculations demonstrate the results of our analysis c 2007 elsevier b v all rights reserved

stabilizing fixed points of time delay systems close to the hopf bifurcation using a dynamic delayed feedback control method this paper deals with the problem of hopf bifurcation control for a class of nonlinear time delay systems a dynamic delayed feedback control method is utilized for stabilizing unstable fixed points near hopf bifurcation using a linear stability analysis we show that under certain conditions of the control parameters and without changing the operating point of the system the onset of hopf bifurcation is delayed meanwhile by applying the center manifold theorem and the normal form theory we obtain formulas for determining the direction of the hopf bifurcation and the stability of bifurcating periodic solutions of the closed loop system numerical simulations are given to justify the validity of the analytical results for the system controlled by the proposed method

shafer hermite pade approximants for functions with exponentially small imaginary part with application to equatorial waves with critical latitude quadratic shafer approximants and their generalization to higher degree polynomials called hermite padeapproximants have been successfully used in quantum mechanics for calculation of exponentially small escape rates in this paper we test quadratic shafer approximants in representing growth rates typical for equatorial atmosphere one of the characteristic features of the equatorial kelvin wave the dominant mode in equatorial dynamics is its exceptionally small linear growth rate for example kelvin wave evolving on the zonal basic state with small linear shear e has growth rate o exp 1 e 2 in contrast to i e o exp 1 e common to similar problems in quantum mechanics it is interesting to know how well hermite pade approximants handle this more computationally expensive problem first we apply the quadratic shafer approximants to calculate the imaginary part of the gauss stieltjes function defined asg s e lim d 0 0 exp t 2t 1 i d edton its branch cut the imaginary part of g s e can be shown to bei g s e pexp 1 e 2 which is of the same order of magnitude as kelvin in shear growth rate next we use this technique to sum the divergent rayleigh schrodinger perturbation series of the hermite with pole equationu y y e11 ey l y 2u 0 which is a simple model for equatorial waves in shear the hermite with pole equation has been previously studied numerically and analytically in j p boyd a nataroc stud appl math 101 1998 43 we compare shafer approximants against numerical integration and find that for small e shafer approximants are more efficient primarily because with rational coefficients one does not need multiple precision at the main stage of the calculation although the higher order approximants are usually more accurate the overall improvement of accuracy is not monotonic due to the appearance of nearly coincident zeros in the approximants

bifurcations in a planar system of differential delay equations modeling neural activity abstract a planar system of differential delay equations modeling neural activity is investigated the stationary points and their saddle node bifurcations are estimated by an analysis of the associated characteristic equation hopf bifurcations are demonstrated at the intersection points of the saddle node and hopf bifurcation curves in an appropriate parameter plane the existence of bogdanov takens singularities is shown the properties of the bogdanov takens singularities are studied by applying the center manifold and normal form theory a numerical example illustrates the obtained results

degree distributions of evolving alphabetic bipartite networks and their projections many real world systems are modeled as evolving bipartite networks and their one mode projections in particular discrete combinatorial systems dcss which consist of a finite set of elementary units and different combinations of these units can be modeled by a subclass of bipartite networks known as alphabetic bipartite networks or a bins where the bottom partite set contains a fixed number of nodes the elementary units and the top partite set grows unboundedly with time through the addition of nodes the combinations the principal questions in the study of a bin evolution are to predict the degree distribution of the bottom set and that of the projection onto the bottom set the bottom projection from a knowledge of the bipartite growth dynamics in this paper we propose a realistic growth model for a bins where the degree distribution of the top set i e the distribution of the number of elementary units in the composite entities in the dcs can be any arbitrary distribution with finite first and second moments utilizing an exact correspondence between the preferential growth of a bins and the polya urn scheme we analytically solve the model to compute exact degree distributions of the bottom fixed set and the bottom projection to the best of our knowledge this is the first work which proposes and solves such a generalized growth model for a bins we also derive that the degree distributions of both the bottom set and the bottom projection suitably normalized with time converge to distributions that are invariant over time we also verify that this improved model can accurately explain the degree distributions of several real world dcss and their projections

generic stabilizability for time delayed feedback control time delayed feedback control is one of the most successful methods to discover dynamically unstable features of a dynamical system in an experiment this approach feeds back only terms that depend on the difference between the current output and the output from a fixed time t ago thus any periodic orbit of period t in the feedback controlled system is also a periodic orbit of the uncontrolled system independent of any modelling assumptions it has been an open problem whether this approach can be successful in general that is under genericity conditions similar to those in linear control theory controllability or if there are fundamental restrictions to time delayed feedback control we show that in principle there are no restrictions this paper proves the following for every periodic orbit satisfying a genericity condition slightly stronger than classical linear controllability one can find control gains that stabilize this orbit with extended time delayed feedback control while the paper s techniques are based on linear stability analysis they exploit the specific properties of linearizations near autonomous periodic orbits in nonlinear systems and are thus mostly relevant for the analysis of nonlinear experiments

nonlinear galerkin methods this article presents a new method of integrating evolution differential equations the non linear galerkin method that is well adapted to the long term integration of such equations while the usual galerkin method can be interpreted as a projection of the considered equation on a linear space the methods considered here are related to the projection of the equation on a nonlinear manifold from the practical point of view some terms have been identified as small and sometimes but not always disregarded

latent geometry of bipartite networks despite the abundance of bipartite networked systems their organizing principles are less studied compared to unipartite networks bipartite networks are often analyzed after projecting them onto one of the two sets of nodes as a result of the projection nodes of the same set are linked together if they have at least one neighbor in common in the bipartite network even though these projections allow one to study bipartite networks using tools developed for unipartite networks one mode projections lead to significant loss of information and artificial inflation of the projected network with fully connected subgraphs here we pursue a different approach for analyzing bipartite systems that is based on the observation that such systems have a latent metric structure network nodes are points in a latent metric space while connections are more likely to form between nodes separated by shorter distances this approach has been developed for unipartite networks and relatively little is known about its applicability to bipartite systems here we fully analyze a simple latent geometric model of bipartite networks and show that this model explains the peculiar structural properties of many real bipartite systems including the distributions of common neighbors and bipartite clustering we also analyze the geometric information loss in one mode projections in this model and propose an efficient method to infer the latent pairwise distances between nodes uncovering the latent geometry underlying real bipartite networks can find applications in diverse domains ranging from constructing efficient recommender systems to understanding cell metabolism