entrainment control in a noisy neural system the open plus closed loop opcl entrainment control put forth by jackson and grosu physica d 85 1995 is applied to an effective neuron system as a way to extract stable limit cycles from a chaotic attractor analogous to the retrieval of memories from a memory searching state additive gaussian white noise representing the natural noise inherent in any real dynamical system is added to the entrainment control mechanism moderate levels of additive noise have little effect on successful entrainment as reflected in phase space plots and lyapunov exponents all three lyapunov exponents are negative which suggests parallels between opcl control and chaotic synchronization al 2

a circle map in a human heart abstract a circle is divided into two regions a black one and a white one successive iterates of an invertible nonlinear circle map generate a symbolic string indicating whether each iterate is in the black or white region a number of remarkable properties of the symbolic sequences are described these properties were previously described for a linear circle map corresponding to a rigid rotation in the gaps and steps problem these results have direct application to a cardiac arrhythmia parasystole that results from the competition between two pacemakers in the heart one in the sinus mode and the other in the ventricles the theoretical results are directly applicable to a clinical case of a young man who had frequent extra heartbeats

the hellinger correlation in this paper the defining properties of any valid measure of the dependence between two continuous random variables are revisited and complemented with two original ones shown to imply other usu

pointwise i convergence and i convergence in measure of sequences of functions let i p n be an ideal we say that a sequence yn n n of real numbers is i convergent to y r if for every neighborhood u of y the set of n s satisfying yn u is in i basing upon this notion we define pointwise i convergence and i convergence in measure of sequences of measurable functions defined on a measure space with finite measure we discuss the relationship between these two convergences in particular we show that for a wide class of ideals including erd s ulam ideals and summable ideals the pointwise i convergence implies the i convergence in measure we also present examples of very regular ideals such that this implication does not hold

shock models with dependence and asymmetric linkages abstract this paper introduces a new class of copulas and shows its relevance for applications in particular a stochastic interpretation in terms of a system of dependence components affected by a global shock is given as a main feature of the model the global shock has an opposite effect on the different components of the system copulas generated by this mechanism are characterized in the bivariate case and their main properties are illustrated connections with concepts like semilinear copulas and conic aggregation functions are also highlighted moreover a high dimensional extension is presented

two neuron dynamics and adiabatic elimination abstract we consider an effective neuron network obtained from the hopfield model by adiabatic elimination the validity of the slaving procedure is first numerically examined the self interaction of the effective neuron network may lead to non zero attractors far from the origin ui 0 the qualitative structure of the attractors for this two effective neuron model with j12j21 0 or

time delay effects on coupled limit cycle oscillators at hopf bifurcation abstract we present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at hopf bifurcation for a simple model consisting of just two oscillators with a time delayed coupling the bifurcation diagram obtained by numerical and analytical solutions shows significant changes in the stability boundaries of the amplitude death phase locked and incoherent regions a novel result is the occurrence of amplitude death even in the absence of a frequency mismatch between the two oscillators similar results are obtained for an array of n oscillators with a delayed mean field coupling and the regions of such amplitude death in the parameter space of the coupling strength and time delay are quantified some general analytic results for the n thermodynamic limit are also obtained and the implications of the time delay effects for physical applications are discussed

a characterization of the orthogonal grid constructions of copulas a framework for constructing copulas that can be regarded as a patchwork like assembly of arbitrary copulas with non overlapping rectangles as patches is studied in de baets b de meyer h 2007 orthogonal grid constructions of copulas ieee trans fuzzy syst 15 1053 1062 where the authors provide sufficient conditions to derive a family of construction methods our aim in this note is to provide a characterization of such constructions msc primary 60e05 secondary 62h20

ortholinear and paralinear semi copulas abstract a new method to construct semi copulas is introduced these semi copulas are called ortholinear resp paralinear semi copulas and their construction is based on linear interpolation on segments that are perpendicular resp parallel to the diagonal of the unit square the classes of ortholinear and paralinear quasi copulas are characterized as well

perturbation of a hopf bifurcation by an external time periodic forcing contenrs i introduction ii the mathematical model iii dynamics of the poincark map in the non resonant and weakly resonant cases iv dynamics of the poincark map in the p l resonant case v dynamics of the poincart map in the p 2 resonant case vi dynamics of the poincark map in the p 3 resonant case

on relation between the ideal core and ideal cluster points abstract this article is motivated by the recent paper characterization of the ideal core by paolo leonetti jmaa 2019 we show that in the main result of that paper the first countability condition can be omitted and the compactness condition may be substituted by a strictly weaker one

zero linear copulas abstract we introduce a new method for constructing copulas c a special type of aggregation functions based on the idea that c u v 0 if u g v for any continuous and decreasing function g 0 1 0 1 such that g 1 0 and c is linear if u g v 1 we also study the relationship between these copulas and other known families of copulas we provide some salient properties and measure the dependence and asymmetry in this class of copulas

copulas diagonals and tail dependence we present some known and novel aspects about bivariate copulas with prescribed diagonal section by highlighting their use in the description of the tail dependence moreover we present the tail concentration function which depends on the diagonal section of a copula as a tool to give a description of tail dependence at finite scale the tail concentration function is hence used to introduce a graphical tool that can help to distinguish different families of copulas in the copula test space moreover it serves as a basis to determine the grouping structure of different financial time series by taking into account their pairwise tail behavior

zero sets of copulas abstract we study conditions on sets in order to be zero sets of semi copulas quasi copulas and with special attention of copulas we find necessary and sufficient conditions for characterizing the zero sets of absolutely continuous copulas and copulas whose support coincides with the closure of the complementary of the zero set moreover we study several topological properties and the lattice theoretic structure and characterize the zero sets of the class of archimedean copulas

stability and bifurcations of equilibria in a multiple delayed differential equation the influence of multiple negative delayed feedback loops on the stability of a single action mechanism are considered a characteristic equation for the linearized stability of the equilibrium is completely analyzed as a function of two parameters describing a delay in one loop and a ratio of the gains in the two feedback loops the bifurcations occurring as the linear stability is lost are analyzed by the construction of a centre manifold in particular the nature of hopf and more degenerate higher codimension bifurcations are explicitly determined

periodic entrainment of chaotic logistic map dynamics consider the map dynamics xn 1 f xn c with a control parameter c let the governing set gn n 0 1 2 be a desired periodic dynamic set gn n gn it is noted that the non autonomous system xn 1 f xn c gn has such a solution xn gn if gn gn 1 f gn c in particular the set of values gn38 might be obtained from the periodic solutions of gn 1 f gn c using suitable values of c this study explores the values of c which yield entrained solutions their basin of entrainment x0 limn xn gn 0 and more generally the basins of bounded solutio ns and their character when f x c cx 1 x the logistic map of particular interest is the entrainment of chaotic dynamics c 4 generally the basin of entrainment for period one governing g0 is x0 1 g0 1 c g0 1 c 2c with the above b asin or if c 1 2c g0 c 4 2c with the basin x 0 g0 x0 1 g0 the complimentary x0 region yields unbounded dynamics period two governing values have two basins depending on the initial value used for g0 these basins are investigated for the sets gn 1 f gn c other periodic sets gn in gn do not become disjoint i n space period four entrainment for suitable c can have even larger basins the unwanted occurrence of other disjoint basins of attraction which interlace the basins of entrainment as a function of both x0 and g0 is discussed other periodic and non periodic responses to these periodic gn are also studied

stability and chaos in an inertial two neuron system abstract inertia is added to a continuous time hopfield 1984 effective neuron system we explore the effects on the stability of the fixed points of the system a two neuron system with one or two inertial terms added is shown to exhibit chaos the chaos is confirmed by lyapunov exponents power spectra and phase space plots

weak statistical convergence and weak filter convergence for unbounded sequences abstract for every weakly statistically convergent sequence x n with increasing norms in a hilbert space we prove that sup n x n n this estimate is sharp we study analogous problem for some other types of weak filter convergence in particular for the erdos ulam filters analytical p filters and f filters we present also a refinement of the recent aron garcia maestre result on weakly dense sequences that tend to infinity in norm

on statistical measure theory abstract the purpose of this paper is to unify various kinds of statistical convergence by statistical measure convergence and to present jordan decomposition of finitely additive measures it is done through dealing with the most generalized statistical convergence ideal convergence by applying geometric functional analysis and banach space theory we first show that for each type of ideal i 2 n convergence there exists a set s of statistical measures such that the measure s convergence is equivalent to the statistical convergence to search for jordan decomposition of measures of statistical type we show that the subspace x i span a a i is an ideal of the space l in the sense of banach lattice hence the quotient space l x i is isometric to a c k space we then prove that a statistical measure has a jordan decomposition if and only if its corresponding functional is norm attaining on l and which in turn induces an approximate null ideal preserved jordan decomposition theorem of finitely additive measures finally we show this characterization and the approximate decomposition theorem are true for finitely additive measures defined on a general measurable space

the distribution of the probability mass of biconic copulas we study the probability mass distribution of biconic copulas provide a counterexample to a result given in jwaid et al 2012 29 concerning a characterization of singular biconic copulas and provide a new one

adaptive control in nonlinear dynamics abstract we extend an adaptive control algorithm recently suggested by huberman and lumer to multi parameter and higher dimensional nonlinear systems this control mechanism is remarkably effective in returning a system to its original dynamics after a sudden perturbation in the system parameters changes the dynamical behaviour we find that in all cases the recovery time is linearly proportional to the inverse of control stiffness for small stiffness in higher dimensions there is an additional optimization problem since increasing stiffness beyond a certain value can retard recovery the control of fixed point dynamics in systems capable of a wide variety of dynamical behaviour is demonstrated we further suggest methods by which periodic motion such as limit cycles can be adaptively controlled and demonstrate the robustness of the procedure in the presence of additive background noise

a generic mechanism for spatiotemporal intermittency a simple mechanism for spatiotemporal intermittency is described it occurs in systems that exhibit bistability between a homogeneous stationary state and an oscillatory one close to parameter values where the oscillation disappears through an andronov homoclinic bifurcation c 1998 elsevier science b v all rights reserved

dimensions and entropies of strange attractors from a fluctuating dynamics approach abstract it is shown that the fluctuations in the divergence of near by trajectories on strictly deterministic strange attractors can be modelled by stochastic concepts in particular we propose kramers moyal type equations for correlation functions between points on the attractor the drift terms are the lyapunov exponents the diffusion terms depend on the above fluctuations from this we obtain bounds on generalized dimensions and entropies numerical results show that in nearly all studied cases henon map zaslavskii map mackey glass eq the attractors are fractal measures in the sense of farmer information dimension hausdorff dimension metric entropy topological entropy

transmitting information by controlling nonlinear oscillators the transmission of information relying on the perturbation of nonlinear oscillators vector fields can be approached in a unified manner this can be accomplished by making use of the information transmission via control principle which is stated and proved in the present work in short this principle establishes that any controller used to identically synchronize pairs of nonlinear oscillators including chaotic ones as a special case can be actually employed as demodulator decoder in the process of information recovery other theoretical results related to the practical realization of the itvc principle are presented and experimental data is provided showing a good agreement with the proposed theory

dynamics control of chaotic systems by parametric destochastization it is shown that deterministic noise chaos appearing via destruction of the quasiperiodic motion may be easily suppressed by weak parametric perturbation of the system

entrainment and migration controls of two dimensional maps a general approach to several types of controls of complex dynamic systems formulated by jackson is applied to two classic two dimensional maps xk 1 e xk x r2 the henon and the ikeda maps the convergent regions of their phase spaces ck are shown to respectively possess translational and rotatational symmetries several topologically distinct entrainment goals e goals gk ck are illustrated for the henon map for both maps the basins of entrainment be g0 x0 limk xk g0 0 of the controlled dynamics for fixed point goals in each convergent region g0 ck are illustrated the be g0 are invariant relative to g0 when g0 is varied by the above symmetries it is proved that for the ikeda map be g0 0 r2 for experimental purposes spheres of entrainment are introduced se r0 x0 x0 g0 r g0 where r g0 maxr r x0 g0 r limk xk g0 0 the ikeda map has two attractors in a bounded region so that migration controls can be illustrated this is done using several migration goals m goals which transfer this system from one attractor to the basin of attraction of the other attractor a1 ba2 or a2 ba1 these require controls only for finite times the influence of noise on the entrainment process is analyzed and compared with numerical examples

the distribution of the probability mass of conic copulas in this note we study the probability mass distribution of conic copulas provide counterexamples to a result given in jwaid et al 21 concerning a characterization of singular conic copulas and provide a new one

multivariate archimedean copulas d monotone functions and l1 norm symmetric distributions it is shown that a necessary and sufficient condition for an archimedean copula generator to generate a d dimensional copula is that the generator is a d monotone function the class of d dimensional archimedean copulas is shown to coincide with the class of survival copulas of d dimensional l 1 norm symmetric distributions that place no point mass at the origin the d monotone archimedean copula generators may be characterized using a little known integral transform of williamson duke math j 23 1956 189 207 in an analogous manner to the well known bernstein widder characterization of completely monotone generators in terms of the laplace transform these insights allow the construction of new archimedean copula families and provide a general solution to the problem of sampling multivariate archimedean copulas they also yield useful expressions for the d dimensional kendall function and kendall s rank correlation coefficients and facilitate the derivation of results on the existence of densities and the description of singular components for archimedean copulas the existence of a sharp lower bound for archimedean copulas with respect to the positive lower orthant dependence ordering is shown

a note on an idempotent transformation of absolutely continuous archimedean copulas abstract in de baets et al 6 the authors define for a copula c an idempotent transformation d c which in some cases generates new copulas in this note we give a negative answer to a question posed in 6 showing that d c is not necessarily a copula when c is an absolutely continuous archimedean copula

turbulent transport and the random occurrence of coherent events abstract we suggest that the transport properties and dissipation rates of a wide class of turbulent flows are determined by the random occurrence of coherent events which correspond to certain orbits which we call homoclinic excursions in the high dimensional strange attractor homoclinic excursions are trajectories in the noncompact phase space that are attracted to special orbits which connect saddle points in the finite region of phase space to infinity and represent organized structures in the flow field this picture also suggests that one can compute fluxes using a relatively low dimensional description of the flow a method for extracting the organized structures from a time series is given and provides a local analogue of the notion of lyapunov exponents

quantifying local predictability in phase space abstract both the classical lyapunov exponents and the quantities from which they are derived the local divergence rates characterize the behavior of initially adjacent trajectories in phase space the exponents are the long term averages of this divergence while the local rates quantify the behavior of nearby trajectories as a function of time and phase space position thus given a transient free initial state the local divergence rates provide estimates of short term predictability along the resultant trajectory we calculate local divergence rates for the chaotic attractor of the three component lorenz model and we investigate both the temporal and phase spatial variations in predictability we show quantitatively that predictability varies considerably with time but that there is phase spatial organization to the variability this underlying structure permits identification of regions in phase space of high and low predictability and in some cases it permits an estimate of predictability to be assigned to the predictability variable itself

controlling transient chaos the method of ott grebogi and yorke 1990 is extended to control transient chaos the controlled signal then exhibits a periodic behaviour which is qualitatively different from that of the actual attractor the time needed to achieve control is shown to be constant and to lie in the order of magnitude of the transient lifetime the number of controlled trajectories however decreases the maximum perturbation according to a power law applicability to experimental situations and comparison with permanent chaotic cases are discussed

an open plus closed loop opcl control of complex dynamic systems a new method of contmlfing arbitrary nonlinear dynamic systems dx dt f x t x c n is presented it is proved that there exists solutions x t in the neighborhood of any arbitrary goal dynamics g t that are entrained to g t through the use of an additive controlling action k g x t h dg dt g c g t g t x which is the sum of the openloop h ibler action h dg dt g and a suitable linear closed lo0p feedback action c g t examples of some newly obtained entrainment capabilities are given for the during and van der pol systems for these and the lorenz and rtssler systems proofs are given for global basins of entrainment for all goal dynamics that can be exponentially bounded in time the basin of entrainment is also established for the chua system as well as the possibility of a coexisting basin of attraction to another fixed point

determining lyapunov exponents from a time series we present the first algorithms that allow the estimation of non negative lyapunov exponents from an experimental time series lyapunov exponents which provide a qualitative and quantitative characterization of dynamical behavior are related to the exponentially fast divergence or convergence of nearby orbits in phase space a system with one or more positive lyapunov exponents is defined to be chaotic our method is rooted conceptually in a previously developed technique that could only be applied to analytically defined model systems we monitor the long term growth rate of small volume elements in an attractor the method is tested on model systems with known lyapunov spectra and applied to data for the belousov zhabotinskii reaction and couette taylor flow

short communication a note on the notion of singular copula we clarify the link between the notion of singular copula and the concept of support of the measure induced by a copula

strong resonances of spatially distributed oscillators a laboratory to study patterns and defects abstract this paper describes phenomena which arise in a continuous system of coupled oscillators subject to a strongly resonant forcing we show that the temporal forcing induces a new type of instability leading to the formation of spatial patterns such as stripes hexagons and spatio temporal intermittent states reminiscent of chemical and magnetical systems we also report the existence of localized states where the instability is confined in the core of a defect leading to an increased mobility and diffusive behaviour of the defect

effects of time delayed position feedback on a van der pol duffing oscillator abstract the mechanism for the action of time delay in a non autonomous system is investigated in this paper the original mathematical model under consideration is a van der pol duffing oscillator with excitation a delayed system is obtained by adding both linear and nonlinear time delayed position feedbacks to the original system functional analysis is used to change the delayed system into a functional differential equation fde the time delay is taken as a variable parameter to investigate its effect on the dynamics of the system such as the stability and bifurcation of an equilibrium point phase locked periodic and phase shifting solution period doubling quasi periodic motion and chaos a periodic solution expressed in the closed form with the aid of the center manifold and averaging theorem is found to be in good agreement with that obtained by numerical simulation two routes to chaos are found namely period doubling bifurcation and torus breaking the results obtained in this paper show that time delay may be used as a simple but efficient switch to control motions of a system either from order motion to chaos or from chaotic motion to order for different applications

on the control of complex dynamic systems a method is described for the limited control of the dynamics of systems which generally have several dynamic attractors associated either with maps or first order ordinary differential equations ode in rn the control is based on the existence of convergent regions cc k 1 2 in the phase space of such systems where there is local convergence of all nearby orbits the character of the control involves the entrainment and subsequent possible migration of the experimental system from one attractor to another entrainment means that limt x t g t 0 where x t rn is the system s controlled dynamics and the goal dynamics g t gk has any topological form but is limited dynamically and to regions of phase space gk contained in some ck gk ck the control process is initiated only when the system enters a basin of entrainment bek gk associated with the goal region gk aside from this macroscopic initial state information about the system no further feedback of dynamic information concerning the response of the system is required the experimental reliability of the control requires that the regions bek be convex regions in the phase space which can apparently be assured if gk ck simple illustrations of these concepts are given using a general linear and a piecewise linear ode in rn in addition to these entrainment goals migration goal dynamics is introduced which intersects two convergent regions g cj g cj i j and permits transferring the dynamics of a system from one attractor to another or from one convergent region to another in the present study these concepts are illustrated with various one dimensional maps involving one or more attractors and convergent regions several theorems concerning entrainment are derived for very general continuous one dimensional maps sufficient conditions are also established which ensure near entrainment for a system when the dynamic model of the system is not exactly known the applications of these concepts to higher dimensional maps and flows will be presented in subsequent studies

a characterization of banach spaces with separable duals via weak statistical convergence abstract let b be a banach space a b valued sequence xk is weakly statistically null provided lim n 1 n k n f x k e 0 for all e 0 and every continuous linear functional f on b a banach space is finite dimensional if and only if every weakly statistically null b valued sequence has a bounded subsequence if b is separable b is separable if and only if every bounded weakly statistically null b valued sequence contains a large weakly null sequence a characterization of spaces containing an isomorphic copy of l1 is given and it is also shown that l2 has a statistical m basis which is not a schauder basis

copulas with continuous strictly increasing singular conditional distribution functions abstract using iterated function systems induced by so called modifiable transformation matrices t and tools from symbolic dynamical systems we first construct mutually singular copulas a t with identical possibly fractal or full support that are at the same time singular with respect to the lebesgue measure 2 on 0 1 2 afterwards the established results are utilized for a simple proof of the existence of singular copulas a t with full support for which all conditional distribution functions y f x a t y are continuous strictly increasing and have derivative zero almost everywhere this result underlines the fact that conditional distribution functions of copulas may exhibit surprisingly irregular analytic behavior finally we extend the notion of empirical copula to the case of non i i d data and prove uniform convergence of the empirical copula e n corresponding to almost all orbits of a markov process usually referred to as chaos game to the singular copula a t several examples and graphics illustrate both the chosen approach and the main results

front motion metastability and subcritical bifurcations in hydrodynamics metastability occurs whenever under given external conditions as defined by the reynolds number in hydrodynamics more than one linearly stable solution may exist in variational problems the preferred state is usually claimed to be the one with the lowest energy but in hydrodynamics and except for very special conditions no energy functional exists from an analogy between amplitude and reaction diffusion equations it is argued that the border separating in space two possible solutions of the flow equations as turbulent and laminar in pipe flows or boundary layers moves with a constant mean velocity depending on the control parameter the sign of this velocity allows to decide which state is stable and which is metastable possible physical implications of these ideas for various problems of hydrodynamics are discussed

algorithms for controlling chaotic motion application for the bvp oscillator the bvp oscillator is a biologically and physically important dynamical system exhibiting chaotic motion phaselocking phenomenon and so on in this paper we investigate the controlling of chaos in this system both when periodic and constant currents are present we use the various control algorithms and investigate their effectiveness in particular we study the controlling by the following mechanisms i adaptive control algorithm ii weak periodic perturbations iii ott grebogi yorke method iv weak feedback control and v addition of noise also we show the suppression of chaos by numerical models

spatiotemporal chaos in the one dimensional complex ginzburg landau equation the dynamical behavior of a large one dimensional system obeying the cubic complex ginzburg landau equation is studied numerically as a function of parameters near a supercritical bifurcation two types of chaotic behavior can be distinguished beyond the benjamin feir instability a phase turbulence regime with a conserved phase winding number and no phase dislocations space time defects and a defect regime with a nonzero density of defects the transition between the two can either be continuous or discontinuous hysteretic depending on parameters the spatial decay of the phase correlation function is inferred to be exponential in both regimes with a sharp decrease of the correlation length upon entering the defect phase the temporal decay of correlations is exponential in the defect regime