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

analysis and design of impulsive control systems some sufficient conditions for asymptotic stability of impulsive control systems with impulses at fixed times have recently been presented in this paper we derive some less conservative conditions for asymptotic stability of such impulsive control systems and the results are used to design impulsive control for a class of nonlinear systems the class of nonlinear systems considered is also extended

hopf bifurcation in a delayed reaction diffusion advection population model abstract in this paper we investigate a reaction diffusion advection model with time delay effect the stability instability of the spatially nonhomogeneous positive steady state and the associated hopf bifurcation are investigated when the given parameter of the model is near the principle eigenvalue of an elliptic operator our results imply that time delay can make the spatially nonhomogeneous positive steady state unstable for a reaction diffusion advection model and the model can exhibit oscillatory pattern through hopf bifurcation the effect of advection on hopf bifurcation values is also considered and our results suggest that hopf bifurcation is more likely to occur when the advection rate increases

hopf bifurcation in a diffusive lotka volterra type system with nonlocal delay effect abstract the dynamics of a diffusive lotka volterra type model for two species with nonlocal delay effect and dirichlet boundary conditions is investigated in this paper the existence and multiplicity of spatially nonhomogeneous steady state solutions are obtained by means of lyapunov schmidt reduction the stability of spatially nonhomogeneous steady state solutions and the existence of hopf bifurcation with the changes of the time delay are obtained by analyzing the distribution of eigenvalues of the infinitesimal generator associated with the linearized system by the normal form theory and the center manifold reduction the stability and bifurcation direction of hopf bifurcating periodic orbits are derived finally our theoretical results are illustrated by a model with homogeneous kernels and one dimensional spatial domain

a note on hopf bifurcations in a delayed diffusive lotka volterra predator prey system the diffusive lotka volterra predator prey system with two delays is reconsidered here the stability of the coexistence equilibrium and associated hopf bifurcation are investigated by analyzing the characteristic equations and our results complement earlier ones we also obtain that in a special case a hopf bifurcation of spatial inhomogeneous periodic solutions occurs in the system

dynamics in a diffusive predator prey system with ratio dependent predator influence abstract a diffusive predator prey system with predator functional response subject to neumann boundary conditions is considered existence nonexistence and boundedness of positive steady state solutions are shown to identify the ranges of parameters of spatial pattern formation hopf and steady state bifurcation analyses are carried out in detail these results provide theoretical evidences to the complex spatio temporal dynamics found by numerical simulation

spatially nonhomogeneous equilibrium in a reaction diffusion system with distributed delay we consider a reaction diffusion system with general time delayed growth rate and kernel functions the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained moreover taking minimal time delay as the bifurcation parameter hopf bifurcation near the steady state solution is proved to occur at a critical value 0 especially the hopf bifurcation is forward and the bifurcated periodic solutions are stable on the center manifold the general results are applied to competitive and cooperative systems with weak or strong kernel function respectively

synchronization control for nonlinear stochastic dynamical networks pinning impulsive strategy in this paper a new control strategy is proposed for the synchronization of stochastic dynamical networks with nonlinear coupling pinning state feedback controllers have been proved to be effective for synchronization control of state coupled dynamical networks we will show that pinning impulsive controllers are also effective for synchronization control of the above mentioned dynamical networks some generic mean square stability criteria are derived in terms of algebraic conditions which guarantee that the whole state coupled dynamical network can be forced to some desired trajectory by placing impulsive controllers on a small fraction of nodes an effective method is given to select the nodes which should be controlled at each impulsive constants the proportion of the controlled nodes guaranteeing the stability is explicitly obtained and the synchronization region is also derived and clearly plotted numerical simulations are exploited to demonstrate the effectiveness of the pinning impulsive strategy proposed in this paper

hopf bifurcations in a reaction diffusion population model with delay effect abstract a reaction diffusion population model with a general time delayed growth rate per capita is considered the growth rate per capita can be logistic or weak allee effect type from a careful analysis of the characteristic equation the stability of the positive steady state solution and the existence of forward hopf bifurcation from the positive steady state solution are obtained via the implicit function theorem where the time delay is used as the bifurcation parameter the general results are applied to a food limited population model with diffusion and delay effects as well as a weak allee effect population model

l2 regularity for parabolic partial integrodifferential equations with delay in the highest order derivatives abstract a partial integrodifferential equation is studied in which the derivatives of highest order also contain a discrete and a distributed delay by means of abstract regularity results global existence and uniqueness of a strict solution are obtained moreover a characterization of the infinitesimal generator of the solution operator is given

the first boundary value problem for strongly elliptic differential difference equations in this chapter we study solvability spectrum and smoothness of generalized solutions of the first boundary value problem for strongly elliptic differential difference equations we also apply these results to the investigation of elliptic differential equations with nonlocal conditions

on a class of retarded partial differential equations on developpe des resultats recents sur des equations d evolution abstraites afin de les appliquer a un type d equations dans des espaces de banach avec un retard discret et continu ces equations peuvent etre considerees comme la version abstraite d equations integrodifferentielles partielles a retard

numerical steady state and hopf bifurcation analysis on the diffusive nicholson s blowflies equation1research partially supported by natural sciences and engineering research council of canada 1 for the dirichlet boundary value problem of the diffusive nicholson s blowflies equation it was shown in ref 17 that in a certain range of the parameter space there is a unique positive steady state solution in this paper we propose a scheme to compute this steady state numerically in addition we describe an iterative procedure to locate the critical values of the delay where a hopf bifurcation of time periodic solutions takes place near the steady state some numerical simulations of both schemes are given

synchronisation of complex dynamical networks with different dynamics of nodes via decentralised dynamical compensation controllers this paper investigates the synchronisation of nonlinear coupled complex dynamical networks with different nonlinear nodes and different orders by using decentralised dynamical compensation controllers we propose a dynamical network mathematical model with similar nonlinear nodes whose dimensions are different for this kind of network model the decentralised dynamical compensation controllers are designed for the state synchronisation of the coupled nodes in addition the synchronisation manifold is defined as an invariant manifold which is regarded as the generalised case of dynamical networks with the same nodes dynamics furthermore some stability criteria for the synchronisation are derived by means of rigorous theoretical analysis finally numerical examples are presented to verify the effectiveness of the obtained theoretical results

hopf bifurcation in a reaction diffusion equation with distributed delay and dirichlet boundary condition abstract the stability and hopf bifurcation of the positive steady state to a general scalar reaction diffusion equation with distributed delay and dirichlet boundary condition are investigated in this paper the time delay follows a gamma distribution function through analyzing the corresponding eigenvalue problems we rigorously show that hopf bifurcations will occur when the shape parameter n 1 and the steady state is always stable when n 0 by computing normal form on the center manifold the direction of hopf bifurcation and the stability of the periodic orbits can also be determined under a general setting our results show that the number of critical values of delay for hopf bifurcation is finite and increasing in n which is significantly different from the discrete delay case and the first hopf bifurcation value is decreasing in n examples from population biology and numerical simulations are used to illustrate the theoretical results

hopf bifurcation of traveling wave solutions of delayed fisher kpp equation the dynamical behavior of the traveling wave front solutions of the delayed fisher kpp equation is studied by employing the theory of functional differential equation it is found that when the delay term t comes through a threshold one equilibrium point is always unstable and there exists a periodic solution near the other equilibrium point in the traveling wave equation by using the theory of center manifold and normal form the stability of the bifurcating periodic solution which corresponds to the periodic traveling wave solution of the original equation is obtained finally some numerical simulations are also given to illustrate our results of theoretical analysis

formulation of the normal form of turing hopf bifurcation in partial functional differential equations abstract turing hopf bifurcation is considered as an important mechanism for generating complex spatio temporal patterns in dynamical systems in this work the normal form up to the third order for the hopf steady state bifurcation which includes the turing hopf bifurcation of a general system of partial functional differential equations pfdes in a bounded spatial region of any dimension is derived based on the center manifold and the normal form theories of pfdes the explicit formula for the coefficients in the normal form of hopf steady state bifurcation are presented concisely in a matrix form which makes it more convenient in not only symbolic derivation but also numerical implementation this provides an approach of showing the existence and stability of stationary and time periodic solutions with spatial heterogeneity the derived formulas are also applicable to partial differential equations and functional differential equations

impulsively control complex networks with different dynamical nodes to its trivial equilibrium this paper investigates the stability of complex networks with different dynamical nodes by impulsive control a model of complex network with different dynamical nodes is presented and then the impulsive controlled network is written as a whole vector equation specially the coupling matrix in this model is not assumed to be diffusive or irreducible some criteria and corollary are derived for the presented impulsive controlled complex networks furthermore the results are illustrated by a complex network composed of the chaotic lorenz systems and chua s circuit systems all the numerical simulations verify the correctness of the theoretical results

stability and hopf bifurcation for a delayed prey predator system with diffusion effects abstract this paper is concerned with a delayed lotka volterra prey predator system with diffusion effects and neumann boundary conditions the main purpose is to investigate the stability of spatially homogeneous positive equilibrium and give the explicit formulae determining the direction and stability of hopf bifurcation by linearizing the system at positive equilibrium and analyzing the associated characteristic equation the stability of positive equilibrium and the existence of hopf bifurcation are demonstrated by means of the normal form theory and the center manifold reduction for partial functional differential equations pfdes the direction and stability of periodic solutions occurring through hopf bifurcation are determined finally in order to verify our theoretical results some numerical simulations are also included

dynamical analysis of a logistic equation with spatio temporal delay this paper is concerned with a logistic equation with spatio temporal delay the local asymptotic behavior of positive constant steady state solution of the equation is considered in particular by using the iterative technique sufficient conditions are established for the existence of traveling wave front solution connecting the zero and the positive constant steady state solution finally numerical simulations supporting the theoretical analysis are also included

convergence to equilibrium in degenerate parabolic equations with delay abstract in 11 busenberg huang 1996 showed that small positive equilibria can undergo supercritical hopf bifurcation in a delay logistic reaction diffusion equation with dirichlet boundary conditions consequently stable spatially inhomogeneous time periodic solutions exist previously in 12 badii diaz tesei 1987 considered a similar logistic type delay diffusion equation but differing in two important respects firstly by the inclusion of nonlinear degenerate diffusion of so called porous medium type and secondly by the inclusion of an additional dominating instantaneous negative feedback where terms local in time majorize the delay terms in some sense sufficient conditions were given ensuring convergence of non negative solutions to a unique positive equilibrium a natural question to ask and one which motivated the present work is can one still ensure convergence to equilibrium in delay logistic diffusion equations in the presence of nonlinear degenerate diffusion but in the absence of dominating instantaneous negative feedback the present paper considers this question and provides sufficient conditions to answer in the affirmative in fact the results are much stronger establishing global convergence for a much wider class of problems which generalize the porous medium diffusion and delay logistic terms to larger classes of nonlinearities furthermore the results obtained are independent of the size of the delay

chaos synchronization of general complex dynamical networks recently it has been demonstrated that many large scale complex dynamical networks display a collective synchronization motion here we introduce a time varying complex dynamical network model and further investigate its synchronization phenomenon based on this new complex network model two network chaos synchronization theorems are proved we show that the chaos synchronization of a time varying complex network is determined by means of the inner coupled link matrix the eigenvalues and the corresponding eigenvectors of the coupled configuration matrix rather than the conventional eigenvalues of the coupled configuration matrix for a uniform network especially we do not assume that the coupled configuration matrix is symmetric and its off diagonal elements are nonnegative which in a way generalizes the related results existing in the literature

brief paper a unified synchronization criterion for impulsive dynamical networks this paper focuses on the problem of globally exponential synchronization of impulsive dynamical networks two types of impulses are considered synchronizing impulses and desynchronizing impulses in previous literature all of the results are devoted to investigating these two kinds of impulses separately thus a natural question arises is there any unified synchronization criterion which is simultaneously effective for synchronizing impulses and desynchronizing impulses in this paper a unified synchronization criterion is derived for directed impulsive dynamical networks by proposing a concept named average impulsive interval the derived criterion is theoretically and numerically proved to be less conservative than existing results numerical examples including scale free and small world structures are given to show that our results are applicable to large scale networks

necessary conditions for partial differential equations with delay to generate c0 semigroups on etudie l existence des solutions ou le caractere bien pose d equations aux derivees partielles a retard du type du t dt f u t ou f est un operateur d un espace de fonction 7b f r 0 y dans l espace de banach y dans lequel l equation evolue

stability and bifurcation in a reaction diffusion model with nonlocal delay effect in this paper the existence stability and multiplicity of spatially nonhomogeneous steady state solution and periodic solutions for a reaction diffusion model with nonlocal delay effect and dirichlet boundary condition are investigated by using lyapunov schmidt reduction moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain

hopf bifurcation for a delayed predator prey diffusion system with dirichlet boundary condition a delayed predator prey diffusion system with beddington deangelis functional response under dirichlet boundary condition is investigated the existence and stability of the positive spatially nonhomogeneous steady state solution are obtained via the implicit function theorem moreover taking feedback time delay as the bifurcation parameter hopf bifurcation near the positive steady state solution is proved to occur at a sequence of critical values we can show that feedback time delay can induce nonhomogeneous periodic oscillatory patterns the direction of hopf bifurcation is forward when parameter m in model 1 2 is sufficiently large numerical simulations and numerical solutions are presented to illustrate our theoretical results

bifurcation of positive solutions for a three species food chain model with diffusion abstract in this paper we consider a reaction diffusion system describing a three species lotka volterra food chain model with homogeneous dirichlet boundary conditions by regarding the birth rate of prey r 1 as a bifurcation parameter the global bifurcation of positive steady state solutions from the semi trivial solution set is obtained via the bifurcation theory the results show that if the birth rate of mid level predator and top predator are located in the regions 0 r 2 1 a 23 u 3 r 3 and r 3 1 respectively then the three species can co exist provided the birth rate of prey exceeds a critical value moreover an explicit expression of coexistence steady state solutions is constructed by applying the implicit function theorem it is demonstrated that the explicit coexistence steady state solutions is locally asymptotically stable

robust h output feedback control for uncertain complex delayed dynamical networks abstract in this paper the robust h control problem of uncertain complex delayed dynamical networks with non identical nodes is investigated the dynamic output feedback controllers are designed to ensure robustly global stability and a smaller prescribed h disturbance attenuation level for the resulting closed loop systems the controller design problem can be solved by a cone complementary linearization algorithm involving linear matrix inequality lmi conditions a numerical example is given to illustrate the effectiveness of the proposed method

stability and hopf bifurcation in a diffusive logistic population model with nonlocal delay effect abstract a reaction diffusion model with logistic type growth nonlocal delay effect and dirichlet boundary condition is considered and combined effect of the time delay and nonlocal spatial dispersal provides a more realistic way of modeling the complex spatiotemporal behavior the stability of the positive spatially nonhomogeneous positive equilibrium and associated hopf bifurcation are investigated for the case of near equilibrium bifurcation point and the case of spatially homogeneous dispersal kernel

a fitted numerical method for a system of partial delay differential equations we consider a system of two coupled partial delay differential equations pddes describing the dynamics of two cooperative species the original system is reduced to a system of ordinary delay differential equations ddes obtained by applying the method of lines then we construct a fitted operator finite difference method fofdm to solve this resulting system the model considered in this paper is very sensitive to small changes in the parameters associated in with the model depending on the values of these parameters the solution can be stable periodic and or aperiodic such behavior of the solution is exploited via the proposed fofdm this fofdm is analyzed for convergence and it is seen that this method is unconditionally stable and has the accuracy of o k h 2 where k and h denote time and space step sizes respectively some numerical results confirming theoretical observations are also presented these results are comparable with those obtained in the literature

integral control for synchronization of complex dynamical networks with unknown non identical nodes this paper proposes a high gain integral controller for synchronization of complex dynamical networks with unknown non identical nodes the integral controller converts the complex dynamical system into a singular perturbation form then a sufficient condition for global synchronization is derived finally the numerical simulation is presented to illustrate the effectiveness of the proposed method

impulsively synchronizing chaotic systems with delay and applications to secure communication in this paper the presence of transmission delay and sampling delay in chaos based secure communication systems by employing impulsive synchronization is studied a time delayed impulsive differential system with delayed impulses modeling the synchronization error between the driving and response schemes employed in such communication systems is presented the equi attractivity property of the error dynamics is investigated and the sufficient conditions leading to this property are obtained a set of upper bounds on the delay terms involved in the system are also obtained and a numerical example is given a communication security scheme employing hyperchaotic systems possessing continuous driving impulsive driving and delay is proposed and simulation results are given to demonstrate the performance of the scheme

permutation p value approximation via generalized stolarsky invariance abstract when it is necessary to approximate a small permutation pvalue p then simulation is very costly for linear statistics a gaussian approximation p1 reduces to the volume of a spherical cap using stolarsky s 1973 invariance principle from discrepancy theory we get a formula for the mean of p1 p 2 over all spherical caps from a theorem of brauchart and dick 2013 we get such a formula averaging only over spherical caps of volume exactly p1 we also derive an improved estimator p2 equal to the average true p value over spherical caps of size p1 containing the original data point x0 on their boundary this prevents p2 from going below 1 n when there are n unique permutations we get a formula for the mean of p2 p 2 and find numerically that the root mean squared error of p2 is roughly proportional to p2 and much smaller than that of p1

controlling the false discovery rate a practical and powerful approach to multiple testing summary the common approach to the multiplicity problem calls for controlling the familywise error rate fwer this approach though has faults and we point out a few a different approach to problems of multiple significance testing is presented it calls for controlling the expected proportion of falsely rejected hypotheses the false discovery rate this error rate is equivalent to the fwer when all hypotheses are true but is smaller otherwise therefore in problems where the control of the false discovery rate rather than that of the fwer is desired there is potential for a gain in power a simple sequential bonferronitype procedure is proved to control the false discovery rate for independent test statistics and a simulation study shows that the gain in power is substantial the use of the new procedure and the appropriateness of the criterion are illustrated with examples

cascades of hopf bifurcations from boundary delay we consider a 1 dimensional reaction diffusion equation with nonlinear boundary conditions of logistic type with delay we deal with non negative solutions and analyze the stability behavior of its unique positive equilibrium solution which is given by the constant function u 1 we show that if the delay is small this equilibrium solution is asymptotically stable similar as in the case without delay we also show that as the delay goes to infinity this equilibrium becomes unstable and undergoes a cascade of hopf bifurcations the structure of this cascade will depend on the parameters appearing in the equation this equation shows some dynamical behavior that differs from the case where the nonlinearity with delay is in the interior of the domain

stability and bifurcations in a nonlocal delayed reaction diffusion population model abstract a nonlocal delayed reaction diffusion equation with dirichlet boundary condition is considered in this paper it is shown that a positive spatially nonhomogeneous equilibrium bifurcates from the trivial equilibrium the stability instability of the bifurcated positive equilibrium and associated hopf bifurcation are investigated providing us with a complete picture of the dynamics

normal forms and hopf bifurcation for partial differential equations with delays the paper addresses the computation of normal forms for some partial functional differential equations pfdes near equilibria the analysis is based on the theory previously developed for autonomous retarded functional differential equations and on the existence of center or other invariant manifolds as an illustration of this procedure two examples of pfdes where a hopf singularity occurs on the center manifold are considered

stability analysis of a stage structure model with spatiotemporal delay effect this paper is concerned with a stage structure model with spatiotemporal delay and homogeneous dirichlet boundary condition the existence of steady state solution bifurcating from the trivial equilibrium is obtained by using lyapunovschmidt reduction the stability analysis of the positive spatially nonhomogeneous steady state solution is investigated by a detailed analysis of the characteristic equation using the properties of the omega limit set we obtain the global convergence of the solution with finite delay

stability and bifurcation in a diffusive lotka volterra system with delay in this paper we investigate the dynamics of a class of diffusive lotka volterra equation with time delay subject to the homogeneous dirichlet boundary condition in a bounded domain the existence of spatially nonhomogeneous steady state solution is investigated by applying lyapunov schmidt reduction the stability and nonexistence of hopf bifurcation at the spatially nonhomogeneous steady state solution with the changes of a specific parameter are obtained by analyzing the distribution of the eigenvalues moreover we illustrate our general results by applications to models with a single delay and one dimensional spatial domain