synchronization in general complex dynamical networks with coupling delays abstract complex networks have attracted increasing attention from various fields of science and engineering today due to the finite speeds of transmission and spreading as well as traffic congestions a signal or influence travelling through a complex network often is associated with time delays and this is very common in biological and physical networks in this paper we introduce complex dynamical network models with coupling delays for both continuous and discrete time cases and then investigate their synchronization phenomena and criteria based on these new complex network models we derive synchronization conditions for both delay independent and delay dependent asymptotical stabilities in terms of linear matrix inequalities lmi we finally use a network with a fixed delay and a specific coupling scheme as an example to illustrate the theoretical results

loop star decomposition of basis functions in the discretization of the efie a general and readily applicable scheme is presented for the determination of the basis functions that allow the decomposition of the surface current into a solenoidal part and a nonsolenoidal remainder the proposed approach brings into correspondence these two parts with two scalar functions and generates the known loop and star basis functions the completeness of the loop star basis is discussed employing the presented scheme the issue of the irrotational property of the nonsolenoidal functions is addressed

synchronization of continuous dynamical networks with discrete time communications in this paper synchronization of continuous dynamical networks with discrete time communications is studied though the dynamical behavior of each node is continuous time the communications between every two different nodes are discrete time i e they are active only at some discrete time instants moreover the communication intervals between every two communication instants can be uncertain and variable by choosing a piecewise lyapunov krasovskii functional to govern the characteristics of the discrete communication instants and by utilizing a convex combination technique a synchronization criterion is derived in terms of linear matrix inequalities with an upper bound for the communication intervals obtained the results extend and improve upon earlier work simulation results show the effectiveness of the proposed communication scheme some relationships between the allowable upper bound of communication intervals and the coupling strength of the network are illustrated through simulations on a fully connected network a star like network and a nearest neighbor network

multisynchronization of coupled heterogeneous genetic oscillator networks via partial impulsive control this paper focuses on the collective dynamics of multisynchronization among heterogeneous genetic oscillators under a partial impulsive control strategy the coupled nonidentical genetic oscillators are modeled by differential equations with uncertainties the definition of multisynchronization is proposed to describe some more general synchronization behaviors in the real considering that each genetic oscillator consists of a large number of biochemical molecules we design a more manageable impulsive strategy for dynamic networks to achieve multisynchronization not all the molecules but only a small fraction of them in each genetic oscillator are controlled at each impulsive instant theoretical analysis of multisynchronization is carried out by the control theory approach and a sufficient condition of partial impulsive controller for multisynchronization with given error bounds is established at last numerical simulations are exploited to demonstrate the effectiveness of our results

stabilization of delay systems delay dependent impulsive control the stabilization problem of delay systems is studied under the delay dependent impulsive control the main contributions of this technical note are that for one thing it shows that time delays in impulse term may contribute to the stabilization of delay systems that is a control strategy which does not work without delay feedback in impulse term can be activated to stabilize some unstable delay systems if there exist some time delay feedbacks for another it shows the robustness of impulsive control that is the designed control strategy admits the existence of some time delays in impulse term which may do harm to the stabilization in this technical note from impulsive control point of view we firstly propose an impulsive delay inequality then we apply it to the delay systems which may be originally unstable and derive some delay dependent impulsive control criteria to ensure the stabilization of the addressed systems the effectiveness of the proposed strategy is evidenced by two illustrative examples

second order design sensitivity analysis of mechanical system dynamics dependence of dynamic response of nonlinear mechanical systems on design variables is analysed an adjoint variable method is used to derive first and second order derivatives of measures of dynamic response with respect to design variables a computational algorithm is presented for numerical calculation of first and second design derivatives a simple oscillator example is solved analytically and by the adjoint variable method with identical results a burst fire automatic weapon mechanism with linear and nonlinear damping is treated numerically it is shown that quadratic appriximations of dynamic response using results of second order design sensitivity analysis can be substantially better than conventional linear approximations

effect of parameter mismatch on the mechanism of chaos synchronization loss in coupled systems using the example of two coupled logistic maps we investigate the effect of nonidentical subsystems on the bifurcations of saddle periodic orbits embedded in a symmetric chaotic attractor these bifurcations determine the process of loss of chaos synchronization we show that if bifurcations conditioned by the symmetry of the system take part in the synchronization loss process nonidentity changes the bifurcation scenario of the transition to a nonsynchronous regime in this case for example the transition to the bubbling behavior is determined not by bifurcation of an orbit embedded in the chaotic attractor but by the smooth shift of it and the saddle repeller bifurcation of the birth of new orbits in the vicinity of the quasisymmetric region s1063 651x 98 10909 1 pacs number s 05 45 1b

h_ infty state estimation for discrete time complex networks with randomly occurring sensor saturations and randomly varying sensor delays in this paper the state estimation problem is investigated for a class of discrete time delay nonlinear complex networks with randomly occurring phenomena from sensor measurements the randomly occurring phenomena include randomly occurring sensor saturations rosss and randomly varying sensor delays rvsds that result typically from networked environments a novel sensor model is proposed to describe the rosss and the rvsds within a unified framework via two sets of bernoulli distributed white sequences with known conditional probabilities rather than employing the commonly used lipschitz type function a more general sector like nonlinear function is used to describe the nonlinearities existing in the network the purpose of the addressed problem is to design a state estimator to estimate the network states through available output measurements such that for all probabilistic sensor saturations and sensor delays the dynamics of the estimation error is guaranteed to be exponentially mean square stable and the effect from the exogenous disturbances to the estimation accuracy is attenuated at a given level by means of an h norm in terms of a novel lyapunov krasovskii functional and the kronecker product sufficient conditions are established under which the addressed state estimation problem is recast as solving a convex optimization problem via the semidefinite programming method a simulation example is provided to show the usefulness of the proposed state estimation conditions

sampled data synchronization of chaotic lur e systems with time delays this paper studies the problem of sampled data control for master slave synchronization schemes that consist of identical chaotic lur e systems with time delays it is assumed that the sampling periods are arbitrarily varying but bounded in order to take full advantage of the available information about the actual sampling pattern a novel lyapunov functional is proposed which is positive definite at sampling times but not necessarily positive definite inside the sampling intervals based on the lyapunov functional an exponential synchronization criterion is derived by analyzing the corresponding synchronization error systems the desired sampled data controller is designed by a linear matrix inequality approach the effectiveness and reduced conservatism of the developed results are demonstrated by the numerical simulations of chua s circuit and neural network

admissible delay upper bounds for global asymptotic stability of neural networks with time varying delays this paper is concerned with global asymptotic stability of a neural network with a time varying delay where the delay function is differentiable uniformly bounded with delay derivative bounded from above first a general reciprocally convex inequality is presented by introducing some slack vectors with flexible dimensions this inequality provides a tighter bound in the form of a convex combination than some existing ones second by constructing proper lyapunov krasovskii functional global asymptotic stability of the neural network is analyzed for two types of the time varying delays depending on whether or not the lower bound of the delay derivative is known third noticing that sufficient conditions on stability from estimation on the derivative of some lyapunov krasovskii functional are affine both on the delay function and its derivative allowable delay sets can be refined to produce less conservative stability criteria for the neural network under study finally two numerical examples are given to substantiate the effectiveness of the proposed method

synchronization analysis of linearly coupled systems described by differential equations with a coupling delay when a transmission delay occurs in the interconnection of linearly coupled systems described by ordinary differential equations lcodes both synchronization and the final synchronized state will vary in this paper mathematical analysis is presented on the synchronization phenomena of lcodes with a single coupling delay criteria are derived for both local and global synchronization it is known that in addition to the dynamical behaviors of the underlying uncoupled system and the coupling configuration the coupling strength and the coupling delay also play key roles on the stability of synchronization both theoretical and numerical analysis indicate that under some conditions if the coupling strength is large enough the coupled system can be completely synchronized for any coupling delay on the other hand in some cases the coupled system can be synchronized if the coupling delay is small enough

an impedance boundary condition efie that is low frequency and refinement stable a discretization of the impedance boundary condition electric field integral equation ibc efie is introduced that 1 yields the correct solution at arbitrarily small frequencies and 2 requires for its solution a number of matrix vector products bounded as the frequency tends to zero and as the mesh density increases the low frequency stabilization is based on a projector based discrete helmholtz splitting rescaling and recombination that depends on the low frequency behavior of both the efie operator and the surface impedance condition the dense mesh stabilization is a modification of the perfect electric conductor operator preconditioning approach taking into account the effect on the singular value spectrum of the ibc term

connection graph stability method for synchronized coupled chaotic systems this paper elucidates the relation between network dynamics and graph theory a new general method to determine global stability of total synchronization in networks with different topologies is proposed this method combines the lyapunov function approach with graph theoretical reasoning in this context the main step is to establish a bound on the total length of all paths passing through an edge on the network connection graph in particular the method is applied to the study of synchronization in rings of 2k nearest neighbor coupled oscillators a rigorous bound is given for the minimum coupling strength sufficient for global synchronization of all oscillators this bound is explicitly linked with the average path length of the coupling graph contrary to the master stability function approach developed by pecora and carroll the connection graph stability method leads to global stability of synchronization and it permits not only constant but also time dependent interaction coefficients in a companion paper blinking model and synchronization in small world networks with a time varying coupling see this issue this method is extended to the blinking model of small world networks where in addition to the fixed 2 k nearest neighbor interactions all the remaining links are rapidly switched on and off independently of each other

exponential synchronization of hybrid coupled networks with delayed coupling this paper investigates exponential synchronization of coupled networks with hybrid coupling which is composed of constant coupling and discrete delay coupling there is only one transmittal delay in the delayed coupling the fact is that in the signal transmission process the time delay affects only the variable that is being transmitted from one system to another then it makes sense to assume that there is only one single delay contributing to the dynamics some sufficient conditions for synchronization are derived based on lyapunov functional and linear matrix inequality lmi in particular the coupling matrix may be asymmetric or nondiagonal moreover the transmittal delay can be different from the one in the isolated system a distinctive feature of this work is that the synchronized state will vary in comparison with the conventional synchronized solution especially the degree of the nodes and the inner delayed coupling matrix heavily influence the synchronized state finally a chaotic neural network is used as the node in two regular networks to show the effectiveness of the proposed criteria

impulsive effects on quasi synchronization of neural networks with parameter mismatches and time varying delay this paper is concerned with the exponential synchronization issue of nonidentically coupled neural networks with time varying delay due to the parameter mismatch phenomena existed in neural networks the problem of quasi synchronization is thus discussed by applying some impulsive control strategies based on the definition of average impulsive interval and the extended comparison principle for impulsive systems some criteria for achieving the quasi synchronization of neural networks are derived more extensive ranges of impulsive effects are discussed so that impulse could either play an effective role or play an adverse role in the final network synchronization in addition according to the extended formula for the variation of parameters with time varying delay precisely exponential convergence rates and quasi synchronization errors are obtained respectively in view of different types impulsive effects finally some numerical simulations with different types of impulsive effects are presented to illustrate the effectiveness of theoretical analysis

quasi synchronization of heterogeneous dynamic networks via distributed impulsive control this paper studies leader follower synchronization in heterogeneous dynamic networks via distributed impulsive control the goal is to drive the followers to approximately synchronize with the leader within a nonzero error bound referred to as quasi synchronization some fundamental and yet challenging problems are addressed 1 how to obtain a tight quasi synchronization error bound 2 how many and which nodes should be controlled 3 how to design the coupling strength to select the pinned nodes and to determine the impulse intervals to optimize the error bound or to achieve quasi synchronization within a prescribed error bound first some general quasi synchronization conditions are derived with explicit expressions of the error bound second the pinning strategy and the coupling strength in achieving quasi synchronization are explored and expressed in term of impulse intervals it is interesting to find that a large coupling strength will destroy synchrony in contrast to continuous pinning control furthermore the common requirement that the leader has a directed path to every node is needed only in the case that the impulse intervals can be arbitrarily small a new concept referred to as impulse pinning controllability is introduced to the case that impulses cannot take place too frequently third an optimization of the error bound is discussed and formulated under a prescribed error bound the design problem of the coupling strength pinned nodes and impulse intervals is solved finally three examples are given to verify the theoretical results

uniform surface integral equation formulation for mixed impedance boundary conditions a numerical approach based on the surface integral equation sie method is developed for the analysis of time harmonic electromagnetic scattering by impenetrable objects equipped with mixed impedance boundary conditions mibcs mibc is an axially anisotropic generalization of the conventional isotropic leontovich impedance boundary condition the developed sie formulation utilizes surface helmholtz decomposition the self dual formulation of yan and jin and loop and star rwg functions a combined field formulation is applied to avoid internal resonances

graph theory based approach for stability analysis of stochastic coupled systems with levy noise on networks in this paper a novel class of stochastic coupled systems with levy noise on networks scslnns is presented both white noise and levy noise are considered in the networks by exploiting graph theory and lyapunov stability theory criteria ensuring p th moment exponential stability and stability in probability of these scslnns are established respectively these principles are closely related to the topology of the network and the perturbation intensity of white noise and levy noise moreover to verify the theoretical results stochastic coupled oscillators with levy noise on a network and stochastic volterra predator prey system with levy noise are performed finally a numerical example about oscillators network is provided to illustrate the feasibility of our analytical results

global synchronization criteria of linearly coupled neural network systems with time varying coupling in this paper global synchronization of linearly coupled neural network nn systems with time varying coupling is investigated the dynamical behavior of the uncoupled system at each node is general which can be chaotic or others the coupling configuration is time varying i e the coupling matrix is not a constant matrix based on lyapunov function method and the specific property of householder transform some criteria for the global synchronization are obtained by these criteria one can verify whether the coupled system with time varying coupling is globally synchronized which is important and useful for both understanding and interpreting synchronization phenomena and designing coupling configuration finally two simulations are given to demonstrate the effectiveness of the theoretical results

on extended dissipativity of discrete time neural networks with time delay in this brief the problem of extended dissipativity analysis for discrete time neural networks with time varying delay is investigated the definition of extended dissipativity of discrete time neural networks is proposed which unifies several performance measures such as the h infty performance passivity l 2 l infty performance and dissipativity by introducing a triple summable term in lyapunov function the reciprocally convex approach is utilized to bound the forward difference of the triple summable term and then the extended dissipativity criterion for discrete time neural networks with time varying delay is established the derived condition guarantees not only the extended dissipativity but also the stability of the neural networks two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results

cheap second order directional derivatives of stiff ode embedded functionals a second order adjoint method is described for calculating directional derivatives of stiff ode embedded functionals the derivation of the general directional second order adjoint equations for point and integral form functionals is presented a numerical procedure for calculating these directional derivatives that is relatively insensitive to the number of parameters is described and showcased by combining automatic differentiation ad to obtain the adjoint and sensitivity equations with the staggered corrector method to solve the sensitivity systems we achieve computational costs noticeably lower than directional finite differences based on a first order adjoint code

discrete second order adjoints in atmospheric chemical transport modeling atmospheric chemical transport models ctms are essential tools for the study of air pollution for environmental policy decisions for the interpretation of observational data and for producing air quality forecasts many air quality studies require sensitivity analyses i e the computation of derivatives of the model output with respect to model parameters the derivatives of a cost functional defined on the model output with respect to a large number of model parameters can be calculated efficiently through adjoint sensitivity analysis while the traditional first order adjoint models give the gradient of the cost functional with respect to parameters second order adjoint models give second derivative information in the form of products between the hessian of the cost functional and a vector representing a perturbation in sensitivity analysis a search direction in optimization an eigenvector etc in this paper we discuss the mathematical foundations of the discrete second order adjoint sensitivity method and present a complete set of computational tools for performing second order sensitivity studies in three dimensional atmospheric ctms the tools include discrete second order adjoints of runge kutta and of rosenbrock time stepping methods for stiff equations together with efficient implementation strategies numerical examples illustrate the use of these computational tools in important applications like sensitivity analysis optimization uncertainty quantification and the calculation of directions of maximal error growth in three dimensional atmospheric ctms

adjoint sensitivity analysis for nonsmooth differential algebraic equation systems an adjoint sensitivity method is presented for nonsmooth semiexplicit differential algebraic equation systems ndaes of index 1 the adjoint sensitivity system is derived for a generalization of mayer type functionals subject to ndae constraints opposed to classical mayer type functionals that depend on the differential and algebraic variables evaluated only at the initial and final times the generalization depends additionally on the evaluation at multiple interior time points the derived adjoint sensitivity method extends and builds on the method for smooth daes by cao et al siam j sci comput 24 2003 pp 1076 1089 and on the method for nonsmooth odes by ruban j comput systems sci internat 36 1997 pp 536 542

mutual synchronization and clustering in randomly coupled chaotic dynamical networks we introduce and study systems of randomly coupled maps rcm where the relevant parameter is the degree of connectivity in the system global almost synchronized states are found equivalent to the synchronization observed in globally coupled maps until a certain critical threshold for the connectivity is reached we further show that not only the average connectivity but also the architecture of the couplings is responsible for the cluster structure observed we analyse the different phases of the system and use various correlation measures in order to detect ordered non synchronized states finally it is shown that the system displays a dynamical hierarchical clustering which allows the definition of emerging graphs

stability of asymmetric hopfield networks in this paper we discuss dynamical behaviors of recurrently asymmetrically connected neural networks in detail we propose an effective approach to study global and local stability of the networks many of well known existing results are unified in our framework which gives much better test conditions for global and local stability sufficient conditions for the uniqueness of the equilibrium point and its stability conditions are given too

second order switching time optimization for nonlinear time varying dynamic systems this technical note gives a method for calculating the first and second derivatives of a cost function with respect to switching times for systems with piecewise second differentiable dynamics differential equations governing the linear and bilinear operators required for calculating the derivatives are presented example optimizations of linear and nonlinear systems are presented as evidence for the value of second order optimization methods one example converges in 33 iterations using second order methods whereas the first order algorithm requires over 30 000 iterations

distributed event triggered cooperative attitude control of multiple groups of rigid bodies on manifold so 3 in this note the distributed event triggered cooperative attitude control of multiple groups of rigid bodies evolved on nonlinear manifold so 3 is investigated the distributed event triggered mechanism is introduced into the controller design to reduce the communication pressure it is verified that the orientations of rigid bodies in each group converge to a common value with zero angular velocities and these common values in all groups achieve an anti consensus configuration under the proposed intra and inter group cooperative control law simulation results show the effectiveness of the proposed method

synchronization error estimation and controller design for delayed lur e systems with parameter mismatches this paper investigates the problem of master slave synchronization of two delayed lur e systems in the presence of parameter mismatches first by analyzing the corresponding synchronization error system synchronization with an error level which is referred to as quasi synchronization is established some delay dependent quasi synchronization criteria are derived an estimation of the synchronization error bound is given and an explicit expression of error levels is obtained second sufficient conditions on the existence of feedback controllers under a predetermined error level are provided the controller gains are obtained by solving a set of linear matrix inequalities finally a delayed chua s circuit is chosen to illustrate the effectiveness of the derived results

exponential h synchronization and state estimation for chaotic systems via a unified model in this paper h synchronization and state estimation problems are considered for different types of chaotic systems a unified model consisting of a linear dynamic system and a bounded static nonlinear operator is employed to describe these chaotic systems such as hopfield neural networks cellular neural networks chua s circuits unified chaotic systems qi systems chaotic recurrent multilayer perceptrons etc based on the h performance analysis of this unified model using the linear matrix inequality approach novel state feedback controllers are established not only to guarantee exponentially stable synchronization between two unified models with different initial conditions but also to reduce the effect of external disturbance on the synchronization error to a minimal h norm constraint the state estimation problem is then studied for the same unified model where the purpose is to design a state estimator to estimate its states through available output measurements so that the exponential stability of the estimation error dynamic systems is guaranteed and the influence of noise on the estimation error is limited to the lowest level the parameters of these controllers and filters are obtained by solving the eigenvalue problem most chaotic systems can be transformed into this unified model and h synchronization controllers and state estimators for these systems are designed in a unified way three numerical examples are provided to show the usefulness of the proposed h synchronization and state estimation conditions

loop star and loop tree decompositions analysis and efficient algorithms a new analysis of the spectral properties of loop star and loop tree decompositions is presented in this work the analysis will shed light on the behavior of these decompositions when used with regular operators such as the magnetic field and the calderon preconditioned electric field integral operators this work will explain the ill conditioning problems reported in literature and will provide a family of efficient algorithms to solve the ill conditioning and regularizing several loop star tree decomposed equations of interest for applications the theory will be corroborated by numerical results that will show the practical impact of the theoretical developments

novel delay dependent master slave synchronization criteria of chaotic lur e systems with time varying delay feedback control this paper is concerned with the issue of master slave synchronization for chaotic lur e systems clss with time varying delay feedback control a novel integral inequality is developed by employing two adjustable parameters which encompasses the celebrated wirtinger s integral inequality and jensen s inequality as two special cases by constructing an augmented lyapunov krasovskii functional lkf taking fully the information time varying delay range into account less conservative delay dependent synchronization criteria are established in the form of linear matrix inequalities lims besides the desired controller gain can be achieved by introducing new nonlinear function conditions which have not been proposed so far finally a numerical example of typical chua s circuit is presented to show the improvements over the existing criteria and the effectiveness of the design approach

a novel approach to synchronization of nonlinearly coupled network systems with delays in this investigation a novel approach to establishing the global synchronization of coupled network systems is presented under this approach individual subsystems can be non autonomous and the coupling configuration is rather general the coupling terms can be non diffusive nonlinear time dependent asymmetric and with time delays with an iteration scheme the problem of synchronization is transformed into solving a corresponding linear system of algebraic equations subsequently delay dependent and delay independent criteria for global synchronization can be established we implement the present approach to analyze synchronization of the fitzhugh nagumo systems under delayed and nonlinear sigmoidal coupling two examples are presented to demonstrate new dynamical scenarios where oscillatory behavior and multistability emerge or are suppressed as the coupled neurons synchronize under the synchronization criterion in addition asynchrony induced by the coupling strength or coupling delay occurs while the synchronization criterion is violated

on the discrete adjoints of adaptive time stepping algorithms we investigate the behavior of adaptive time stepping numerical algorithms under the reverse mode of automatic differentiation ad by differentiating the time step controller and the error estimator of the original algorithm reverse mode ad generates spurious adjoint derivatives of the time steps the resulting discrete adjoint models become inconsistent with the adjoint ode and yield incorrect derivatives to regain consistency one has to cancel out the contributions of the non physical derivatives in the discrete adjoint model we demonstrate that the discrete adjoint models of one step explicit adaptive algorithms such as the runge kutta schemes can be made consistent with their continuous counterparts using simple code modifications furthermore we extend the analysis to cover second order adjoint models derived through an extra forward mode differentiation of the discrete adjoint code several numerical examples support the mathematical derivations

a time varying complex dynamical network model and its controlled synchronization criteria today complex networks have attracted increasing attention from various fields of science and engineering it has been demonstrated that many complex networks display various synchronization phenomena in this note we introduce a time varying complex dynamical network model we then further investigate its synchronization phenomenon and prove several network synchronization theorems especially we show that synchronization of such a time varying dynamical network is completely determined by the inner coupling matrix and by the eigenvalues and the corresponding eigenvectors of the coupling configuration matrix of the network

on a well conditioned electric field integral operator for multiply connected geometries all known integral equation techniques for simulating scattering and radiation from arbitrarily shaped perfect electrically conducting objects suffer from one or more of the following shortcomings i they give rise to ill conditioned systems when the frequency is low ii and or when the discretization density is high iii their applicability is limited to the quasi static regime iv they require a search for global topological loops v they suffer from numerical cancellations in the solution when the frequency is very low this work presents an equation that does not suffer from any of the above drawbacks when applied to smooth and closed objects the new formulation is obtained starting from a helmholtz decomposition of two discretizations of the electric field integral operator obtained by using rwgs and dual bases respectively the new decomposition does not leverage loop and star tree basis functions but projectors that derive from them following the decomposition the two discretizations are combined in a calderon like fashion resulting in a new overall equation that is shown to exhibit self regularizing properties without suffering from the limitations of existing formulations numerical results show the usefulness of the proposed method both for closed and open structures

solving ibc cfie with dual basis functions the surface integral equation method is applied to solve electromagnetic scattering by arbitrarily shaped three dimensional imperfectly conducting objects modeled with the leontovitch impedance boundary condition ibc dual basis functions are used to remove previously reported difficulties associated with the solution of the combined field integral equation for objects with the ibc by expanding the magnetic current with quasi curl conforming dual functions and the electric current with divergence conforming primary rwg functions leads to a stable discretization procedure for the rotation n operator required by the ibc

transcritical riddling in a system of coupled maps the transition from fully synchronized behavior to two cluster dynamics is investigated for a system of n globally coupled chaotic oscillators by means of a model of two coupled logistic maps an uneven distribution of oscillators between the two clusters causes an asymmetry to arise in the coupling of the model system while the transverse period doubling bifurcation remains essentially unaffected by this asymmetry the transverse pitchfork bifurcation is turned into a saddle node bifurcation followed by a transcritical riddling bifurcation in which a periodic orbit embedded in the synchronized chaotic state loses its transverse stability we show that the transcritical riddling transition is always hard for this we study the sequence of bifurcations that the asynchronous point cycles produced in the saddle node bifurcation undergo and show how the manifolds of these cycles control the magnitude of asynchronous bursts in the case where the system involves two subpopulations of oscillators with a small mismatch of the parameters the transcritical riddling will be replaced by two subsequent saddle node bifurcations or the saddle cycle involved in the transverse destabilization of the synchronized chaotic state may smoothly shift away from the synchronization manifold in this way the transcritical riddling bifurcation is substituted by a symmetry breaking bifurcation which is accompanied by the destruction of a thin invariant region around the symmetrical chaotic state

robust synchronization of an array of coupled stochastic discrete time delayed neural networks this paper is concerned with the robust synchronization problem for an array of coupled stochastic discrete time neural networks with time varying delay the individual neural network is subject to parameter uncertainty stochastic disturbance and time varying delay where the norm bounded parameter uncertainties exist in both the state and weight matrices the stochastic disturbance is in the form of a scalar wiener process and the time delay enters into the activation function for the array of coupled neural networks the constant coupling and delayed coupling are simultaneously considered we aim to establish easy to verify conditions under which the addressed neural networks are synchronized by using the kronecker product as an effective tool a linear matrix inequality lmi approach is developed to derive several sufficient criteria ensuring the coupled delayed neural networks to be globally robustly exponentially synchronized in the mean square the lmi based conditions obtained are dependent not only on the lower bound but also on the upper bound of the time varying delay and can be solved efficiently via the matlab lmi toolbox two numerical examples are given to demonstrate the usefulness of the proposed synchronization scheme

synchronization in an array of linearly coupled networks with time varying delay abstract this paper studies the dynamics of a system of linearly coupled identical connected neural networks with time varying delay some sufficient conditions for synchronization of such a system are obtained based on lyapunov functional method and matrix inequality techniques which can be checked numerically very efficiently by using the matlab toolbox finally an example is provided to demonstrate the effectiveness of the proposed results

adaptation of nonlinear systems through dynamic entropy estimation we show that adaptation and control of the target system can be achieved by linking the modification of its dynamical properties to the estimated difference of the distribution of the dynamical characteristics of the control and target signals subsequently the target system which has initially different dynamical properties adjusts its dynamics via changes of its control parameters and synchronizes with the control one the differences in the evolving probability distributions are evaluated through entropy estimation causing the adaptation to be based solely on the statistical properties of the control and target signals without explicit knowledge of the underlying equations of the system

extended dissipative synchronization of complex dynamical networks with additive time varying delay and discrete time information abstract the problem of extended dissipativity analysis of complex dynamical networks with additive time varying delays and discrete time information is considered in this article by utilizing the lyapunov functional method jensen s inequality and free weighting matrix analysis techniques we established sufficient criterion such that the complex dynamical networks is synchronized further the extended dissipativity analysis problem which contains h performance passivity performance and l 2 l performance in a unified framework is studied the derived criteria are expressed in terms of linear matrix inequalities that can be easily checked by using the standard numerical softwares illustrative examples are presented to demonstrate the effectiveness and usefulness of the proposed results

universality for the parameter mismatching effect on weak synchronization in coupled chaotic systems to examine the universality for the parameter mismatching effect on weak chaotic synchronization we study coupled multidimensional invertible systems such as the coupled henon maps and coupled pendula by generalizing the method proposed in coupled one dimensional 1d noninvertible maps we introduce the parameter sensitivity exponent to measure the degree of the parameter sensitivity of a weakly stable synchronous chaotic attractor in terms of the parameter sensitivity exponents we characterize the effect of the parameter mismatch on the intermittent bursting and the basin riddling occurring in the regime of weak synchronization it is thus found that the scaling exponent for the average characteristic time i e the average interburst time and the average chaotic transient lifetime for both the bubbling and riddling cases is given by the reciprocal of the parameter sensitivity exponent as in the simple system of coupled 1d maps hence the reciprocal relation i e 1 seems to be universal in the sense that it holds in typical coupled chaotic systems of different nature

global stability analysis for stochastic coupled systems on networks this paper considers the global stability problem for some stochastic coupled systems on networks scsns we provide a systematic method for constructing a global lyapunov function for these scsns by using graph theory and the lyapunov second method consequently a new global stability principle which has a close relation to the topology property of the network is given as an application to the results we employ the principle to two well known coupled systems in physical and ecology and then some easy verified sufficient conditions which guarantee the global stability are obtained

projective synchronization of delayed neural networks with mismatched parameters and impulsive effects in this paper the impulsive effects on projective synchronization between the parameter mismatched neural networks with mixed time varying delays have been analyzed since complete synchronization is not possible due to the existence of parameter mismatch and projective factor a drive has been taken to achieve the weak projective synchronization of different neural networks under impulsive control strategies through the use of matrix measure technique and the extended comparison principle based on the formula of variation of parameters for mixed time varying delayed impulsive systems sufficient criteria have been derived for exponential convergence of the networks under the effects of extensive range of impulse instead of upper or lower bound of the impulsive interval the concept of the average impulsive interval is applied to estimate the number of impulsive points in an interval the concept of calculus is applied for optimizing the synchronization error bounds which are obtained because of different ranges of impulse finally the numerical simulations for various impulsive ranges for different cases are presented graphically to validate the efficiency of the theoretical results

distributed h state estimation for stochastic delayed 2 d systems with randomly varying nonlinearities over saturated sensor networks in this paper the distributed h state estimation problem is investigated for the two dimensional 2 d time delay systems the target plant is characterized by the generalized fornasini marchesini 2 d equations where both stochastic disturbances and randomly varying nonlinearities rvns are considered the sensor measurement outputs are subject to saturation restrictions due to the physical limitations of the sensors based on the available measurement outputs from each individual sensor and its neighboring sensors the main purpose of this paper is to design distributed state estimators such that not only the states of the target plant are estimated but also the prescribed h disturbance attenuation performance is guaranteed by defining an energy like function and utilizing the stochastic analysis as well as the inequality techniques sufficient conditions are established under which the augmented estimation error system is globally asymptotically stable in the mean square and the prescribed h performance index is satisfied furthermore the explicit expressions of the individual estimators are also derived finally numerical example is exploited to demonstrate the effectiveness of the results obtained in this paper

exponential synchronization of coupled stochastic memristor based neural networks with time varying probabilistic delay coupling and impulsive delay this paper deals with the exponential synchronization of coupled stochastic memristor based neural networks with probabilistic time varying delay coupling and time varying impulsive delay there is one probabilistic transmittal delay in the delayed coupling that is translated by a bernoulli stochastic variable satisfying a conditional probability distribution the disturbance is described by a wiener process based on lyapunov functions halanay inequality and linear matrix inequalities sufficient conditions that depend on the probability distribution of the delay coupling and the impulsive delay were obtained numerical simulations are used to show the effectiveness of the theoretical results

forward and adjoint sensitivity analysis with continuous explicit runge kutta schemes abstract we study the numerical solution of tangent linear first and second order adjoint models with high order explicit continuous runge kutta pairs the approaches currently implemented in popular packages such as sundials or daspkadjoint are based on linear multistep methods for adaptive time integration of nonlinear models interpolation of the forward model solution is required during the adjoint model simulation we propose to use the dense output mechanism built in the continuous runge kutta schemes as a highly accurate and cost efficient interpolation method in the inverse problem run we implement our approach in a fortran library called denserks which is found to compare well to other similar software on a number of test problems