global analysis of multi host and multi vector epidemic models abstract we formulate a multi group and multi vector epidemic model in which hosts dynamics is captured by staged progression s e i r framework and the dynamics of vectors is captured by an si framework the proposed model describes the evolution of a class of zoonotic infections where the pathogen is shared by m host species and transmitted by p arthropod vector species in each host the infectious period is structured into n stages with a corresponding infectiousness parameter to each vector species we determine the basic reproduction number r 0 2 m n p and investigate the dynamics of the systems when this threshold is less or greater than one we show that the dynamics of the multi host multi stage and multi vector system is completely determined by the basic reproduction number and the structure of the host vector network configuration particularly we prove that the disease free equilibrium is globally asymptotically stable gas whenever r 0 2 m n p 1 and a unique strongly endemic equilibrium exists and is gas if r 0 2 m n p 1 and the host vector configuration is irreducible that is either the disease dies out or persists in all hosts and all vector species

the construction of preconditioners for elliptic problems by substructuring i in earlier parts of this series of papers we constructed preconditioners for the discrete systems of equations arising from the numerical approximation of elliptic boundary value problems the resulting algorithms are well suited for implementation on computers with parallel architecture in this paper we will develop a technique which utilizes these earlier methods to derive even more efficient preconditioners the iterative algorithms using these new preconditioners converge to the solution of the discrete equations with a rate that is independent of the number of unknowns these preconditioners involve an incomplete chebyshev iteration for boundary interface conditions which results in a negligible increase in the amount of computational work theoretical estimates and the results of numerical experiments are given which demonstrate the effectiveness of the methods

stability analysis of a delayed multi group sis epidemic model with nonlinear incidence rates and patch structure abstract in this paper we focus on a delayed multi group sis epidemic model with nonlinear incidence rates and patch structure in which the effects of time delay and population exchange between groups are considered by using a lyapunov functional approach we establish that the global stability of the model is completely determined by a threshold parameter r 0 that is the disease free equilibrium of the model is globally asymptotically stable if r 0 1 while an endemic equilibrium of the model is such if r 0 1 moreover in the analysis we offer new techniques to prove the permanence and the existence of the endemic equilibrium of delayed nonlinear multi group epidemic models this result shows that the incidence delay and the migration delay do not alter the quality of the disease dynamics

asymptotically autonomous semiflows chain recurrence and lyapunov functions from the work of c conley it is known that the omega limit set of a precompact orbit of an autonomous semiflow is a chain recurrent set here we improve a result of l markus by showing that the omega limit set of a solution of an asymptotically autonomous semiflow is a chain recurrent set relative to the limiting autonomous semiflow in the special case that there is a lyapunov function for the limiting semiflow sufficient conditions are given for an omega limit set of the asymptotically autonomous semiflow to be contained in a level set of the lyapunov function

dynamics of a multigroup sis epidemic model with standard incidence rates and markovian switching abstract in this paper we investigate a multigroup sis epidemic model with standard incidence rates and markovian switching first of all we establish sufficient conditions for extinction of the diseases then we obtain sufficient conditions for persistence in the mean of the diseases in addition in the case of persistence we obtain sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic lyapunov function with regime switching

competitive lotka volterra population dynamics with jumps abstract this paper considers competitive lotka volterra population dynamics with jumps the contributions of this paper are as follows a we show that a stochastic differential equation sde with jumps associated with the model has a unique global positive solution b we discuss the uniform boundedness of the p th moment with p 0 and reveal the sample lyapunov exponents c using a variation of constants formula for a class of sdes with jumps we provide an explicit solution for one dimensional competitive lotka volterra population dynamics with jumps and investigate the sample lyapunov exponent for each component and the extinction of our n dimensional model

domain decomposition methods for large linearly elliptic three dimensional problems abstract the idea of solving large problems using domain decomposition technique appears particularly attractive on present day large scale parallel computers but the performance of such techniques used on a parallel computer depends on both the numerical efficiency of the proposed algorithm and the efficiency of its parallel implementation the approach proposed herein splits the computational domain in unstructured subdomains of arbitrary shape and solves for unknown on the interface using the associated trace operator the steklov poincare operator on the continuous level or the schur complement matrix after a finite element discretization and a preconditioned conjugate gradient method this algorithm involves the solution of dirichlet and of neumann problems defined on each subdomain and which can be solved in parallel this method has been implemented on a cray 2 computer using multitasking and on an intel hypercube it was tested on a large scale industrial ill conditioned three dimensional linear elasticity problem which gives a fair indication of its performance in a real life environment in such situations the proposed method appears operational and competitive on both machines compared to standard techniques it yields faster results with far less memory requirements

two group sir epidemic model with stochastic perturbation a stochastic two group sir model is presented in this paper the existence and uniqueness of its nonnegative solution is obtained and the solution belongs to a positively invariant set furthermore the globally asymptotical stability of the disease free equilibrium is deduced by the stochastic lyapunov functional method if r 0 1 which means the disease will die out while if r 0 1 we show that the solution is fluctuating around a point which is the endemic equilibrium of the deterministic model in time average in addition the intensity of the fluctuation is proportional to the intensity of the white noise when the white noise is small we consider the disease will prevail at last we illustrate the dynamic behavior of the model and their approximations via a range of numerical experiments

analysis of stochastic two prey one predator model with levy jumps abstract taking white noises and levy noises into account a two prey one predator model in random environments is proposed and investigated under some simple assumptions the critical value between persistence in the mean and extinction for each population is obtained then sufficient conditions for stability in distribution of the model are established finally some numerical examples are introduced to validate the analytical findings

the existence of inner synchronized stationary distribution for stochastic coupled systems on networks abstract this paper is concerned with the existence of inner synchronized stationary distribution for stochastic coupled systems on networks scsns which is the first time to consider this problem compared with the existing results on inner synchronization problem we study the problem based on lyapunov method and kirchhoff s matrix tree theorem in graph theory without utilizing kronecker product method and linear matrix inequalities which simplifies some complex analysis and avoids difficulties then some new sufficient conditions are presented to guarantee the existence of inner synchronized stationary distribution for scsns these conditions show that the existence domain of inner synchronized stationary distribution has a close relationship with stochastic perturbation intensity and when stochastic perturbation vanishes inner synchronized stationary distribution will become complete synchronization to illustrate the practicability of theoretical results an application about stochastic coupled oscillators is given with a numerical example being carried out

harmonic oscillator under levy noise unexpected properties in the phase space a harmonic oscillator under the influence of noise is a basic model of various physical phenomena under gaussian white noise the position and velocity of the oscillator are independent random variables which are distributed according to the bivariate gaussian distribution with elliptic level lines the distribution of phase is homogeneous none of these properties hold in the general levy case thus the level lines of the joint probability density are not elliptic the coordinate and the velocity of the oscillator are strongly dependent and this dependence is quantified by introducing the corresponding parameter width deficit the distribution of the phase is inhomogeneous and highly nontrivial

stability analysis for coupled systems with time delay on networks abstract in this paper the stability problem for some coupled systems with time delay on networks csdns is investigated we provide a systematic method for constructing a global lyapunov functional for csdns by using graph theory the stability uniform stability and global uniform stability of the systems are investigated and by using the lyapunov functional constructed some sufficient conditions of stability are obtained

global dynamic analysis of a model for vector borne diseases on bipartite networks abstract in this paper an sis si model on bipartite networks for vector borne disease is developed the basic reproduction number r 0 is identified and analyzed the global dynamics are completely determined by the reproduction number r 0 it is shown that if r 0 1 the disease free equilibrium is globally asymptotically stable if r 0 1 there is a unique endemic equilibrium which is globally asymptotically stable finally numerical simulations are performed to validate the theoretical results and reveal the influence of network structure on basic reproduction number the transmission scale and propagation speed

two group infection age model including an application to nosocomial infection in this article we analyze the global asymptotic behavior of a two group si susceptible infected epidemic model with age of infection we prove that the model exhibits the traditional threshold behavior where the disease free equilibrium is globally asymptotically stable if the basic reproduction number is less than one and the endemic equilibrium is globally asymptotically stable if the basic reproduction number is greater than one we conclude the paper by presenting an application to nosocomial infections moreover some numerical simulations are presented for this application

lyapunov functions and global stability for age structured hiv infection model we study the basic age structured population model describing the hiv infection process which is defined by pdes the model allows the production rate of viral particles and the death rate of productively infected cells to vary and depend on the infection age by using the direct lyapunov method and constructing suitable lyapunov functions dynamical properties of the age structured model without or with drug treatment are established the results show that the global asymptotic stability of the infection free steady state and the infected steady state depends only on the basic reproductive number determined by the burst size further we establish mathematically that the typical ode and dde delay differential equation models of hiv infection are equivalent to two special cases of the above pde models

pth moment stability analysis of stochastic recurrent neural networks with time varying delays this paper addresses in great detail the issue of pth moment exponential stability of stochastic recurrent neural networks with time varying delays with the help of the dini derivative of the expectation of v t x t along the solution x t of the model and the technique of halanay type inequality some novel sufficient conditions on pth moment exponential stability of the trivial solution has been established results of the development as presented in this paper are more general than those reported in some previously published papers an example is also given to illustrate that our results are correct and effectiveness

on the dynamics of a class of multi group models for vector borne diseases abstract the resurgence of vector borne diseases is an increasing public health concern and there is a need for a better understanding of their dynamics for a number of diseases e g dengue and chikungunya this resurgence occurs mostly in urban environments which are naturally very heterogeneous particularly due to population circulation in this scenario there is an increasing interest in both multi patch and multi group models for such diseases in this work we study the dynamics of a vector borne disease within a class of multi group models that extends the classical bailey dietz model this class includes many of the proposed models in the literature and it can accommodate various functional forms of the infection force for such models the vector host host vector contact network topology gives rise to a bipartite graph which has different properties from the ones usually found in directly transmitted diseases under the assumption that the contact network is strongly connected we can define the basic reproductive number r 0 and show that this system has only two equilibria the so called disease free equilibrium dfe and a unique interior equilibrium usually termed the endemic equilibrium ee that exists if and only if r 0 1 we also show that if r 0 1 then the dfe equilibrium is globally asymptotically stable while when r 0 1 we have that the ee is globally asymptotically stable

a random attractor for a stochastic second order lattice system with random coupled coefficients abstract in this paper we mainly focus on the asymptotic behavior of solutions to the second order stochastic lattice equations with random coupled coefficients and multiplicative white noises in weighted spaces of infinite sequences we first transfer stochastic lattice equations into random lattice equations and prove the existence and uniqueness of solutions which generate a random dynamical system second we consider the existence of a tempered random bounded absorbing set and a random attractor for the system then we establish the upper semicontinuity of random attractors as the coefficient of the white noise term tends to zero finally we present the corresponding results for the system with additive white noises

stability of stochastic levy noise coupled systems with mixed delays in this paper based on razumikhin method stability of stochastic levy noise coupled systems with mixed delays slcsd is researched here both mixed delays and levy noise are considered into cou

lyapunov coupled equations for continuous time infinite markov jump linear systems this paper deals with lyapunov equations for continuous time markov jump linear systems mjls out of the bent which wends most of the literature on mjls we focus here on the case in which the markov chain has a countably infinite state space it is shown that the infinite mjls is stochastically stabilizable ss if and only if the associated countably infinite coupled lyapunov equations have a unique norm bounded strictly positive solution it is worth mentioning here that this result do not hold for mean square stabilizability mss since ss and mss are no longer equivalent in our set up see e g j baczynski optimal control for continuous time lq problems with infinite markov jump parameters ph d thesis federal university of rio de janeiro ufrj coppe 2000 to some extent a decomplexification technique and tools from operator theory in banach space and in particular from semigroup theory are the very technical underpinning of the paper

environmental variability in a stochastic epidemic model abstract in this paper we investigate the stochastic dynamics of a simple epidemic model incorporating the mean reverting ornstein uhlenbeck process analytically and numerically we define two threshold parameters the stochastic demographic reproduction number r d s and the stochastic basic reproduction number r 0 s to utilize in identifying the stochastic extinction and persistence of the disease we find that the stochastic disease dynamics can be determined by the environment fluctuations which measured by the intensity of volatility and the speed of reversion the larger intensity of volatility or the smaller speed of reversion can suppress the outbreak of the disease the smaller intensity of volatility or the the higher speed of reversion can enhance the outbreak of the disease furthermore via numerical simulations we find that the stochastic model has an endemic stationary distribution which leads to the stochastic persistence of the disease our results show that mean reverting process is a well established way of introducing stochastic environmental noise into biologically realistic population dynamic models

network synchronization diffusion and the paradox of heterogeneity many complex networks display strong heterogeneity in the degree connectivity distribution heterogeneity in the degree distribution often reduces the average distance between nodes but paradoxically may suppress synchronization in networks of oscillators coupled symmetrically with uniform coupling strength here we offer a solution to this apparent paradox our analysis is partially based on the identification of a diffusive process underlying the communication between oscillators and reveals a striking relation between this process and the condition for the linear stability of the synchronized states we show that for a given degree distribution the maximum synchronizability is achieved when the network of couplings is weighted and directed and the overall cost involved in the couplings is minimum this enhanced synchronizability is solely determined by the mean degree and does not depend on the degree distribution and system size numerical verification of the main results is provided for representative classes of small world and scale free networks

letter to the editor adaptive control for modified projective synchronization of a four dimensional chaotic system with uncertain parameters this article is concerned with the modified projective synchronization problem for a class of four dimensional chaotic system with uncertain parameters by utilizing lyapunov method an adaptive control scheme for the synchronization has been presented the control performances are verified by a numerical simulation

stability analysis in lagrange sense for a non autonomous cohen grossberg neural network with mixed delays abstract the paper discusses the global exponential stability in the lagrange sense for a non autonomous cohen grossberg neural network cgnn with time varying and distributed delays the boundedness and global exponential attractivity of non autonomous cgnn with time varying and distributed delays are investigated by constructing appropriate lyapunov like functions moreover we provide verifiable criteria on the basis of considering three different types of activation function which include both bounded and unbounded activation functions these results can be applied to analyze monostable as well as multistable biology neural networks due to making no assumptions on the number of equilibria meanwhile the results obtained in this paper are more general and challenging than that of the existing references in the end an illustrative example is given to verify our results

a continuation ratio random effects model for repeated ordinal responses this paper presents methods of analysis for ordinal repeated measures we use a generalization of the continuation ratio model with a random effect we handle frailty by using a normal distribution and also a non parametric distribution the methodology is readily implemented in existing software and flexible enough to treat large data sets with uncommon time measurements as well as different numbers of repeated measures for each individual the models are used to investigate how a group of explanatory variables influences the overall condition of patients treated for breast cancer

exponential stability of numerical solutions for a class of stochastic age dependent capital system with poisson jumps recently numerical solutions of stochastic differential equations have received a great deal of attention numerical approximation schemes are invaluable tools for exploring their properties in this paper we introduce a class of stochastic age dependent vintage capital system with poisson jumps we also give the discrete approximate solution with an implicit euler scheme in time discretization using gronwall s lemma and barkholder davis gundy s inequality some criteria are obtained for the exponential stability of numerical solutions to the stochastic age dependent capital system with poisson jumps it is proved that the numerical approximation solutions converge to the analytic solutions of the equations under the given conditions where information on the order of approximation is provided these error bounds imply strong convergence as the timestep tends to zero a numerical example is used to illustrate the theoretical results

complete delay decomposing approach to asymptotic stability for neural networks with time varying delays this paper is concerned with the problem of stability of neural networks with time varying delays a novel lyapunov krasovskii functional decomposing the delays in all integral terms is proposed by exploiting all possible information and considering independent upper bounds of the delay derivative in various delay intervals some new generalized delay dependent stability criteria are established which are different from the existing ones and improve upon previous results numerical examples are finally given to demonstrate the effectiveness and the merits of the proposed method

stabilization of multi group models with multiple dispersal and stochastic perturbation via feedback control based on discrete time state observations abstract this paper focuses on the multi group models with multiple dispersal and stochastic perturbation mgmds the effect of both multiple dispersal among groups and stochastic perturbation are taken into consideration the stabilization of mgmds is investigated via feedback control based on the discrete time state observations in addition a systematic method is given to construct a global lyapunov function for mgmds by means of graph theory and lyapunov method some sufficient conditions are obtained to ensure the stabilization in the sense of mean square asymptotical stability an upper bound of the duration between two consecutive state observations is estimated moreover to show the applicability of our results the main theory is employed to a stochastic coupled oscillators finally a numerical example is given to illustrate the effectiveness and feasibility of the theoretical results

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

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

modelling ordered categorical data recent advances and future challenges this article summarizes recent advances in the modelling of ordered categorical ordinal response variables we begin by reviewing some models for ordinal data introduced in the literature in the past 25 years we then survey recent extensions of these models and related methodology for special types of applications such as for repeated measurement and other forms of clustering we also survey other aspects of ordinal modelling such as small sample analyses power and sample size considerations and availability of software throughout we suggest problem areas for future research and we highlight challenges for statisticians who deal with ordinal data

stationary distribution for stochastic coupled systems with regime switching and feedback control abstract the existence of stationary distribution for stochastic coupled systems with regime switching and feedback control is investigated in terms of model feedback control is concerned in the existence of stationary distribution for stochastic coupled systems with regime switching in terms of method graph theory is employed to investigate the existence of stationary distribution for stochastic coupled systems with regime switching and some sufficient conditions are given based on lyapunov method connected with the graph theory and the m matrix method to ensure the existence of stationary distribution which reveals the influences that feedback control brings on stationary distribution and the existing area is related to stochastic disturbance feedback control and coupling strength furthermore the application to stochastic coupled oscillators with feedback control and regime switching can demonstrate the practicability of our theoretical results finally a numerical example is presented to verify the effectiveness and availability of our results as well as the superiority of influence that feedback control brings on stationary distribution

global stability of infectious disease models using lyapunov functions two systematic methods are presented to guide the construction of lyapunov functions for general infectious disease models and are thus applicable to establish their global dynamics specifically a matrix theoretic method using the perron eigenvector is applied to prove the global stability of the disease free equilibrium while a graph theoretic method based on kirchhoff s matrix tree theorem and two new combinatorial identities are used to prove the global stability of the endemic equilibrium several disease models in the literature and two new cholera models are used to demonstrate the applications of these methods

dynamic analysis of stochastic cohen grossberg neural networks with time delays abstract in this paper we discuss stochastic cohen grossberg neural networks with time delays by constructing suitable lyapunov functional and employing the semimartingale convergence theorem we give some sufficient criteria ensuring almost sure exponential stability of the networks the results obtained are helpful to design stability of networks when stochastic noise is taken into consideration

global stability of a multi group sis epidemic model with varying total population size in this paper to analyze the effect of the cross patch infection between different groups to the spread of gonorrhea in a community we establish the complete global dynamics of a multi group sis epidemic model with varying total population size by a threshold parameter in the proof we use special lyapunov functional techniques not only one proposed by the paper pruss et al 2006 but also the other one for a varying total population size with some ideas specified to our model and no longer need a grouping technique derived from the graph theory which is commonly used for the global stability analysis of multi group epidemic models

population averaged and cluster specific models for clustered ordinal response data we compare population averaged and cluster specific models for clustered ordinal data we consider generalized estimating equations and constrained equations maximum likelihood estimation of population averaged cumulative logit regression models and mixed effects estimation of cluster specific cumulative logit regression models a previously reported relationship between population averaged and cluster specific parameters for the binary logistic link appears to hold for analogous parameters under the cumulative logit link we address these issues in the context of data from two cross over clinical trials

global stability problem for coupled systems of differential equations on networks the global stability problem of equilibria is investigated for coupled systems of differential equations on networks using results from graph theory we develop a systematic approach that allows one to construct global lyapunov functions for large scale coupled systems from building blocks of individual vertex systems the approach is applied to several classes of coupled systems in engineering ecology and epidemiology and is shown to improve existing results

stability in delayed cohen grossberg neural networks lmi optimization approach in this paper stability problems are further discussed for a class of delayed cohen grossberg neural networks on the basis of the linear matrix inequality lmi optimization approach and also the lyapunov krasovskii functional method combined with the halanay inequality technique several new sufficient criteria are given for ascertaining the global asymptotic stability and exponential stability of the equilibrium point for this system the proposed results are less restrictive than those given in the earlier literature and are easier to verify in practice in addition four examples and their numerical simulations are given two of them are used to demonstrate the effectiveness of the proposed results and another two show that there exist stable bifurcating periodic solutions if the given conditions do not hold

the stability of stochastic coupled systems with time varying coupling and general topology structure we introduce a class of novel stochastic coupled systems in which the coupling structure is time varying and the topology structure is not strongly connected and first establish the system on a digraph with a time varying weight matrix motivated by du and li 2014 we give a hierarchical method to deal with digraphs without strong connectivity and establish the corresponding hierarchical algorithm to realize this approach also an example is given to illustrate our hierarchical algorithm and its feasibility in the sequel based on the theory of asymptotically autonomous systems kirchhoff s matrix tree theorem and lyapunov method several moment exponential stability criteria are presented including a lyapunov type theorem and a coefficient type criterion furthermore theoretical results are applied to stochastic coupled oscillators with time varying coupling structure sctcs and the stability criterion of sctcs is obtained finally the effectiveness of theoretical results is illustrated by two numerical examples

stochastic population dynamics driven by levy noise abstract this paper considers stochastic population dynamics driven by levy noise the contributions of this paper lie in that a using the khasminskii mao theorem we show that the stochastic differential equation associated with our model has a unique global positive solution b applying an exponential martingale inequality with jumps we discuss the asymptotic pathwise estimation of such a model

a stochastic differential equation sis epidemic model incorporating ornstein uhlenbeck process abstract in this paper based on the results of gray et al 2011 we propose a new sde sis model incorporating mean reverting ornstein uhlenbeck process and prove that the stochastic basic reproduction number r 0 s can be used to identify the stochastic extinction and persistence for the sde mode if r 0 s 1 under mild extra conditions the disease will be extinct a s while if r 0 s 1 the disease will persist a s epidemiologically we find that smaller speed of reversion or bigger intensity of volatility can suppress the disease outbreak thus in order to control the spread of the disease we must decrease the speed of reversion or increase the intensity of volatility

exponential stability of stochastic complex networks with multi weights based on graph theory abstract in this paper a novel approach to exponential stability of stochastic complex networks with multi weights is investigated by means of the graph theoretical method new sufficient conditions are provided to ascertain the moment exponential stability and almost surely exponential stability of stochastic complex networks with multiple weights it is noted that our stability results are closely related with multi weights and the intensity of stochastic disturbance numerical simulations are also presented to substantiate the theoretical results

control of a class of pendulum like systems with lagrange stability in this paper the control problem of linear perturbed systems is investigated some strategies of controller design guaranteeing the closed loop systems with property of pendulum like and lagrange stability are proposed the given method is applied to the system of synchronous single phase motor with pulsing vibrating moment

an evaluation of the solution of linear systems arising from 3d elasticity problems abstract this paper presents the results of different linear system solvers on a cray2 the methods implemented include direct methods preconditioned conjugate gradient based on incomplete factorization and domain decomposition factors that affect the performance such as coloring are also discussed results based on numerical experiments on problems arising from 3d elasticity show the relative merits of the different methods

optimal harvesting policy of logistic population model in a randomly fluctuating environment abstract in this paper we investigate the optimal harvest policy of a stochastic logistic population model the value of this study lies in two aspects mathematically we establish a stochastic threshold theorem to govern whether the population persists or not in the case of population persistence we prove the existence uniqueness and global asymptotic stability of the invariant density of the fokker planck equation associated with the sde model and we further show the relation between these two models in addition we give the unique optimal harvesting effort and the corresponding maximum of expectation of sustainable yield which gives us the profile of the optimal harvesting policy of the sde model ecologically we find that big harvesting effort or big intensity of noise will lead the population to extinct risk almost surely in addition we find that under a fixed randomness strategy and proper harvesting the maximum sustainable yield increases systematically as the harvesting effort increases but overexploitation will reduce the level of maximize sustainable yield and eventually make the whole population extinct with probability one hence in order to obtain the optimal harvesting policy we must decrease the harvesting effort and the intensity of noise furthermore we find that our parameter perturbation method in this paper is more beneficial to the exploitation of renewable resources than the classical one given by beddington and may 1977 the results show that different perturbation method can exhibit different stochastic population dynamics

global stability of multigroup epidemic model with group mixing and nonlinear incidence rates in this paper we introduce a basic reproduction number for a multigroup seir model with nonlinear incidence of infection and nonlinear removal functions between compartments then we establish that global dynamics are completely determined by the basic reproduction number r0 it shows that the basic reproduction number r0 is a global threshold parameter in the sense that if it is less than or equal to one the disease free equilibrium is globally stable and the disease dies out whereas if it is larger than one there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population finally two numerical examples are also included to illustrate the effectiveness of the proposed result

global stability of the endemic equilibrium in infinite dimension lyapunov functions and positive operators abstract the global stability of the endemic equilibrium is shown for an endemic model with infinite dimensional population structure using a volterra like lyapunov function and the krein rutman theorem

power flow analysis of complex coupled systems by progressive approaches a generalized mobility impedance power flow mathematical model is developed to analyze the dynamical behaviour of a complex coupled system consisting of any number of substructures with various configurations and multiple interaction interfaces the coupled system is subject to multiple excitations and selected boundary conditions generalized mobility impedance matrix formulations for three dimensional rigid and elastic structures of general configuration are first derived allowing the construction of equivalent mobility emm and equivalent impedance eim matrices to describe the dynamical behaviour of a substructure or a subsystem assembled from several inter connected substructures within the overall system based on these two proposed matrices two progressive approaches are developed to predict the force vectors and velocity response vectors as well as the power flows into and transmission between substructures in the complex coupled system the developed mathematical model avoids the generalized inverse process associated with rectangular matrices when dealing with multi input multi output mimo systems in which the dimensions of input and output are different it is also very flexible and conveniently extended if additional substructures are further connected to the original dynamic system without involving much additional computational effort the proposed methods are shown to reduce the complexity of the power flow analysis applied to complex dynamic coupled systems and they are applicable to a very large class of dynamical systems in engineering to illustrate and demonstrate their usage the dynamics of a flexible raft vibration isolation system is investigated this comprises two machines flexible raft and flexible foundation with connecting isolator attachments

finite time synchronization of multi coupling stochastic fuzzy neural networks with mixed delays via feedback control abstract in this paper the finite time synchronization problem for multi coupling fuzzy cellular neural networks fcnns with stochastic perturbations and mixed delays is addressed compared with exponential synchronization and asymptotic synchronization in existing literature finite time synchronization of stochastic fcnns is studied for the first time which is of better significance combining graph theoretical technique and lyapunov method under the framework of feedback control some finite time synchronization conditions are derived besides from the perspective of the connectedness of fcnns we just demand at least one directed path on the digraph between different vertices in networks instead of each sub network then the convergence time is explicitly proposed which is connected with the parameters of control and topological structure of networks eventually a numerical example is also carried out to demonstrate the practicability and validity of our proposed results furthermore a secure communication synchronization problem is presented to illustrate the effectiveness of the obtained results

asymptotic synchronization in n dimensional second order dissipative lattices of coupled oscillators abstract by introducing a new norm which is equivalent to the usual norm in the phase space we prove that for n dimensional second order dissipative lattices of coupled oscillators with external periodic forces under dirichlet neumann and periodic boundary conditions if the system is bounded dissipative and the coupled coefficients are both large enough the asymptotic synchronization will occur and we give a concrete bounded dissipative second order lattices system our results show that the bounds of the difference between the components of any solution are directly proportional to m n 2 and inversely proportional to the coupled coefficients where m is the mesh size and n is the space dimension of lattice points

impact of network connectivity on the synchronization and global dynamics of coupled systems of differential equations abstract the global dynamics of coupled systems of differential equations defined on an interaction network are investigated local dynamics at each vertex when interactions are absent are assumed to be simple solutions to each vertex system are assumed to converge to an equilibrium either on the boundary or in the interior of the feasible region the interest is to investigate the collective behaviours of the coupled system when interactions among vertex systems are present it was shown in li and shuai 2010 that if the interaction network is strongly connected then solutions to the coupled system synchronize at a single equilibrium we focus on the case when the underlying network is not strongly connected and the coupled system may have mixed equilibria whose coordinates are in the interior at some vertices while on the boundary at others we show that solutions on a strongly connected component of the network will synchronize considering a condensed digraph by collapsing each strongly connected component we are able to introduce a partial order on the set p of all equilibria and show that all solutions of the coupled system converge to a unique equilibrium p that is the maximizer in p we further establish that behaviours of the coupled system at minimal elements of the condensed digraph determine whether the global limit p is a mixed equilibrium the theory are applied to mathematical models from epidemiology and spatial ecology

discrete time stochastic control systems a continuous lyapunov function implies robustness to strictly causal perturbations abstract discrete time stochastic systems employing possibly discontinuous state feedback control laws are addressed allowing discontinuous feedbacks is fundamental for stochastic systems regulated for instance by optimization based control laws we introduce generalized random solutions for discontinuous stochastic systems to guarantee the existence of solutions and to generate enough solutions to get an accurate picture of robustness with respect to strictly causal perturbations under basic regularity conditions the existence of a continuous stochastic lyapunov function is sufficient to establish that asymptotic stability in probability for the closed loop system is robust to sufficiently small state dependent strictly causal worst case perturbations robustness of a weaker stochastic stability property called recurrence is also shown in a global sense in the case of state dependent perturbations and in a semiglobal practical sense in the case of persistent perturbations an example shows that a continuous stochastic lyapunov function is not sufficient for robustness to arbitrarily small worst case disturbances that are not strictly causal our positive results are also illustrated by examples

global stability of two group sir model with random perturbation abstract in this paper we discuss the two group sir model introduced by guo li and shuai h b guo m y li z shuai global stability of the endemic equilibrium of multigroup sir epidemic models can appl math q 14 2006 259 284 allowing random fluctuation around the endemic equilibrium we prove the endemic equilibrium of the model with random perturbation is stochastic asymptotically stable in the large in addition the stability condition is obtained by the construction of lyapunov function finally numerical simulations are presented to illustrate our mathematical findings

stability of complex valued impulsive stochastic functional differential equations on networks with markovian switching abstract this paper investigates the stability problem of complex valued impulsive stochastic functional differential equations on networks with markovian switching cisfnm markovian switching and impulsive effects are considered into complex valued systems for the first time by virtue of complex generalized ito s formula the stability of cisfnm can be analyzed effectively without splitting the real and imaginary parts then based on razumikhin technique graph theoretical technique as well as average dwell time approach several novel stability criteria are derived which mainly depend on integral average value of time varying coefficients compared with some existing results our results gain not only less conservativeness but also lower calculation complexity subsequently the stability of complex valued impulsive stochastic networks with time varying delays and markovian switching is studied as an application complex valued coupled oscillators are considered and numerical simulations are also presented to show the effectiveness of our main results

global stability of multi group epidemic models with distributed delays abstract we investigate a class of multi group epidemic models with distributed delays we establish that the global dynamics are completely determined by the basic reproduction number r 0 more specifically we prove that if r 0 1 then the disease free equilibrium is globally asymptotically stable if r 0 1 then there exists a unique endemic equilibrium and it is globally asymptotically stable our proof of global stability of the endemic equilibrium utilizes a graph theoretical approach to the method of lyapunov functionals

global dynamics of a general class of multistage models for infectious diseases we propose a general class of multistage epidemiological models that allow possible deterioration and amelioration between any two infected stages the models can describe disease progression through multiple latent or infectious stages as in the case of hiv and tuberculosis amelioration is incorporated into the models to account for the effects of antiretroviral or antibiotic treatment the models also incorporate general nonlinear incidences and general nonlinear forms of population transfer among stages under biologically motivated assumptions we derive the basic reproduction number r 0 and show that the global dynamics are completely determined by r 0 if r 0 leq 1 the disease free equilibrium is globally asymptotically stable and the disease dies out if r 0 1 then the disease persists in all stages and a unique endemic equilibrium is globally asymptotically stable

solution of the stability problem for a class of generalized volterra prey predator systems where ei pij and qj are real constants ui are real valued continuous functions of t for t 0 and zii dui dt both equations are required for i 1 2 m condition lb is here considered to be a restriction on the vector e ei rather than on the matrix p pii as is more usual the hypothesis 0 0 qi 0 is appropriate in applications but as far as the mathematical development is concerned it could be replaced by qiui 0 0 a discussion of historical background can be found in the papers 4 5 to which the present paper is a sequel suffice it to say here that the chief landmarks are volterra s book 6 la salle s theorem 1 21 and krikorian s analysis of the case n 3 3 references 4 5 provide useful

qualitative theory of compartmental systems dynamic models of many processes in the biological and physical sciences which depend on local mass balance conditions give rise to systems of ordinary differential equations many nonlinear that are called compartmental systems in this paper the authors define compartmental systems specify their relations to other nonnegative systems and discuss examples of applications the authors review the qualitative results on linear and nonlinear compartmental systems including their relation to cooperative systems they review the results for linear compartmental systems and then integrate and expand the results on nonlinear compartmental systems providing a framework for unifying them under a few general theorems in the course of that they complete the solution of a problem posed by bellman and show that closed nonlinear autonomous n compartment systems can show the full gamut of possible behaviors of systems of odes finally to provide additional structure to this study the authors show how to partiti

global analysis of new malaria intrahost models with a competitive exclusion principle in this paper we propose a malaria within host model with k classes of age for the parasitized red blood cells and n strains for the parasite we provide a global analysis for this model a competitive exclusion principle holds if mathcal r 0 the basic reproduction number satisfies mathcal r 0 leq 1 then the disease free equilibrium is globally asymptotically stable on the contrary if mathcal r 0 1 then generically there is a unique endemic equilibrium which corresponds to the endemic stabilization of the most virulent parasite strain and to the extinction of all the other parasites strains we prove that this equilibrium is globally asymptotically stable on the positive orthant if a mild sufficient condition is satisfied

existence of limit cycles for coupled van der pol equations abstract in this paper we consider the existence of limit cycles of coupled van der pol equations by using s1 degree theory due to dylawerski et al see ann polon math 62 1991 243

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

global stability of the endemic equilibrium of multigroup sir models with nonlinear incidence in this paper we introduce a basic reproduction number for a multigroup epidemic model with nonlinear incidence then we establish that global dynamics are completely determined by the basic reproduction number r 0 it shows that the basic reproduction number r 0 is a global threshold parameter in the sense that if it is less than or equal to one the disease free equilibrium is globally stable and the disease dies out whereas if it is larger than one there is a unique endemic equilibrium which is globally stable and thus the disease persists in the population finally a numerical example is also included to illustrate the effectiveness of the proposed result

population dynamical behavior of lotka volterra system under regime switching in this paper we investigate a lotka volterra system under regime switching dx t diag x 1 t x n t b r t a r t x t dt s r t db t where b t is a standard brownian motion the aim here is to find out what happens under regime switching we first obtain the sufficient conditions for the existence of global positive solutions stochastic permanence and extinction we find out that both stochastic permanence and extinction have close relationships with the stationary probability distribution of the markov chain the limit of the average in time of the sample path of the solution is then estimated by two constants related to the stationary distribution and the coefficients finally the main results are illustrated by several examples

stability of model based networked control systems with time varying transmission times in model based networked control systems mb ncss an explicit model of the plant is used to produce an estimate of the plant state behavior between transmission times in this paper the stability of mb ncss is studied when the controller actuator is updated with the sensor information at nonconstant time intervals networked control systems with transmission times that are varying either within a time interval or are driven by a stochastic process with identically independently distributed and markov chain driven transmission times are studied sufficient conditions for lyapunov stability are derived for stochastically modeled transmission times almost sure stability and mean square sufficient conditions for stability are introduced

the stability of stochastic coupled systems with time delays and time varying coupling structure this paper is concerned with the pth moment exponential stability of stochastic coupled systems with time delays and time varying coupling structure sctvcs the coupling structure is time varying first second the method of graph theory has been generalized from a system established on a digraph with constant coupling structure to a digraph with time varying coupling structure successfully combining graph theory with lyapunov method a systematic method is given to construct a lyapunov function for sctvcs several pth moment exponential stability criteria are presented including a lyapunov type theorem and some sufficient criteria in the form of coefficients furthermore the theoretical conclusions are applied to the stochastic coupled oscillators with time varying coupling structure and two stability criteria are obtained finally we give two numerical examples to illustrate the effectiveness of our results