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

quantization for nonparametric regression the authors discuss quantization or clustering of nonparametric regression estimates the main tools developed are oracle inequalities for the rate of convergence of constrained least squares estimates these inequalities yield fast rates for both nonparametric unconstrained least squares regression and clustering of partition regression estimates and plug in empirical quantizers the bounds on the rate of convergence generalize known results for bounded errors to subgaussian too

the existence and global exponential stability of periodic solution for a neutral coupled system on networks with delays in this paper we establish sufficient conditions for the existence and global exponential stability of periodic solution to a type of neutral coupled system on networks with delays the key to prove the existence of periodic solutions is using the combined method of graph theory coincidence degree theory and lyapunov functional method and the sufficient conditions are easy to be checked finally a numerical simulation is carried out to show the correctness of our main results

strange attractors in coupled reaction diffusion cells abstract a numerical study of two identical reaction cells with diffusion coupling has shown that the structure of motion in the system in principle agrees with results reported for variety of dynamic systems when the characteristic parameter is varied alternating sub intervals of stable periodic p k and stable aperiodic a l solutions appear the sub intervals are connected by intervals where tangent bifurcations and infinite sequences of subharmonic bifurcations occur feigenbaum relation holds for the studied sequence of subharmonic bifurcations aperiodic chaotic states are characterized by a complete set of one dimensional lyapunov exponents by power spectra and by corresponding poincare maps the spectra of lyapunov exponents are of the type 0 and show that the topological dimension of the chaotic attractor is two the power spectra are of two different types a the spectra with sharp peaks located above the broad band noise showing statistical phase coherence of the attractor b the flat spectra showing only broad band noise corresponding to phase incoherent attractor the phase coherence is present close after every point of accumulation phase incoherence arises when the strange attractors contain unstable periodic orbits with different topology the relations of bifurcated stable and unstable periodic solutions computed by means of continuation techniques to the structure of the strange attractor is discussed and poincare maps are used to illustrate the dependence of the structure of the attractors on the value of the characteristic parameter

abundance of strange attractors in 1976 he h non performed a numerical study of the family of diffeomorphisms of the plane ha b x y 1 ax2 y bx and detected for parameter values a l 4 b 0 3 what seemed to be a non trivial attractor with a highly intricate geometric structure this family has since then been the subject of intense research both numerical and theoretical but its dynamics is still far from being completely understood in particular one could not exclude the possibility that the attractor observed by h6non were just a periodic orbit with a very high period recently in a remarkable paper bc2 benedicks and carleson were able to show that this is not the case at least for a positive lebesgue measure set of parameter values near a 2 b o more precisely they showed that if b 0 is small enough then for a positive measure set of a values near a 2 the corresponding diffeomorphism ha b exhibits a strange attractor their argument is a very creative extension of the techniques they had previously developed in bull for the study of the quadratic family on the real line and no doubt it will be important for the understanding of several other situations of complicated nonhyperbolic dynamics when acquainted in 1985 with the work by benedicks and carleson then in progress palls suggested that one should in this context think of the h6non family as a particular although important model for the creation of a horseshoe and that the emphasis should be put on the occurrence of unfoldings of homoclinic tangencies he proposed that the correct setting for benedicks carleson s results is within this more general framework of homoclinic bifurcations and stated the following

shil nikov configurations in any generic unfolding of the nilpotent singularity of codimension three on r3 abstract we are interested in the dynamics arising in generic unfoldings of the nilpotent singularity of codimension three since shil nikov type homoclinic orbits make up the simplest scenario where very complicated dynamics for three dimensional vector fields can be shown the aim of this paper is to prove analytically their existence in any of such unfoldings

k vectors an alternating minimization algorithm for learning regression functions the k vectors algorithm for learning regression functions proposed here is akin to the well known k means algorithm both algorithms partition the feature space but unlike the k means algorithm the k vectors algorithm aims to reconstruct the response rather than the feature the partitioning rule of the algorithm is based on maximizing the correlation inner product of the feature vector with a set of k vectors and generates polyhedral cells similar to the ones generated by the nearest neighbor rule of the k means algorithm similarly to k means the learning algorithm alternates between two types of steps in the first type of steps k labels are determined via a centroid type rule in the response space which uses a surrogate hinge type loss function to the mean squared error loss function in the second type of steps the k vectors which determine the partition are updated according to a multiclass classification rule in the spirit of support vector machines it is proved that both steps of the algorithm only require solving convex optimization problems and that the algorithm is empirically consistent as the length of the training sequence increases to infinity fixed points of the empirical version of the algorithm tend to fixed points of the population version of the algorithm learnability of the predictor class posit by the algorithm is also established

efficient agnostic learning of neural networks with bounded fan in we show that the class of two layer neural networks with bounded fan in is efficiently learnable in a realistic extension to the probably approximately correct pac learning model in this model a joint probability distribution is assumed to exist on the observations and the learner is required to approximate the neural network which minimizes the expected quadratic error as special cases the model allows learning real valued functions with bounded noise learning probabilistic concepts and learning the best approximation to a target function that cannot be well approximated by the neural network the networks we consider have real valued inputs and outputs an unlimited number of threshold hidden units with bounded fan in and a bound on the sum of the absolute values of the output weights the number of computation steps of the learning algorithm is bounded by a polynomial in 1 spl epsiv 1 spl delta n and b where spl epsiv is the desired accuracy spl delta is the probability that the algorithm fails n is the input dimension and b is the bound on both the absolute value of the target which may be a random variable and the sum of the absolute values of the output weights in obtaining the result we also extended some results on iterative approximation of functions in the closure of the convex hull of a function class and on the sample complexity of agnostic learning with the quadratic loss function

stability analysis of a fractional order diffused prey predator model with prey refuges abstract in this paper a fractional order diffused prey predator model with prey refuges is considered the existence uniqueness non negativity and boundedness of the solutions for the model are proved moreover some sufficient conditions are given to ensure the existence and uniform asymptotic stability of the equilibrium point of the studied system finally numerical simulations are presented in order to support the theoretical results

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

the dynamics of the henon map the purpose of this paper is to develop machinery which is suitable for a study of the long time behavior of systems such as the henon map with expansion combined with strong contraction our study is modeled on the treatment of the one dimensional system x 1 ax 2 and we study the perturbation of a from the value a 2 and b small a surprising number of complications arise when b 0 the computer simulations give some indication of the complicated structure of the attractor but it can safely be stated that the real difficulties do not show up the central aim of the paper is to introduce what we consider the relevant concepts and techniques needed to study mappings such as the henon one

individual convergence rates in empirical vector quantizer design we consider the rate of convergence of the expected distortion redundancy of empirically optimal vector quantizers earlier results show that the mean squared distortion of an empirically optimal quantizer designed from n independent and identically distributed i i d source samples converges uniformly to the optimum at a rate of o 1 spl radic n and that this rate is sharp in the minimax sense we prove that for any fixed distribution supported on a given finite set the convergence rate is o 1 n faster than the minimax lower bound where the corresponding constant depends on the source distribution for more general source distributions we provide conditions implying a little bit worse o logn n rate of convergence although these conditions in general are hard to verify we show that sources with continuous densities satisfying certain regularity properties similar to the ones of pollard that were used to prove a central limit theorem for the code points of the empirically optimal quantizers are included in the scope of this result in particular scalar distributions with strictly log concave densities with bounded support such as the truncated gaussian distribution satisfy these conditions

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

almost sure exponential stabilization of hybrid stochastic coupled systems via intermittent noises a higher order nonlinear growth condition abstract in this paper the almost sure exponential stabilization problem of hybrid coupled systems with two independent noises is investigated wherein one of the noises exists periodically intermittently different from existing literature on coupled systems the functions in the system we addressed are nonlinear without the linear growth condition by employing graph theory and lyapunov method almost sure exponential stabilization criterion of hybrid coupled systems with two independent noises is derived the criterion is closely associated with the noise strength the number of vertex systems the coupling strength the existence interval and period of intermittent noises meanwhile the theoretical results are applied to a higher order nonlinear stochastic coupled electronic oscillators system and the corresponding numerical example is presented

a central limit theorem for k means clustering a set of n points in euclidean space is partitioned into the k groups that minimize the within groups sum of squares under the assumption that the n points come from independent sampling on a fixed distribution conditions are found to assure asymptotic normality of the vector of means of the k groups the method of proof makes novel application of a functional central limit theorem for empirical processes a generalization of donsker s theorem due to dudley

consensus of multiagent systems with distance dependent communication networks in this paper we study the consensus problem of discrete time and continuous time multiagent systems with distance dependent communication networks respectively the communication weight between any two agents is assumed to be a nonincreasing function of their distance first we consider the networks with fixed connectivity in this case the interaction between adjacent agents always exists but the influence could possibly become negligible if the distance is long enough we show that consensus can be reached under arbitrary initial states if the decay rate of the communication weight is less than a given bound second we study the networks with distance dependent connectivity it is assumed that any two agents interact with each other if and only if their distance does not exceed a fixed range with the validity of some conditions related to the property of the initial communication graph we prove that consensus can be achieved asymptotically third we present some applications of the main results to opinion consensus problems and formation control problems finally several simulation examples are presented to illustrate the effectiveness of the theoretical findings

the existence of a stationary distribution for stochastic coupled oscillators abstract this paper addresses a stochastic coupled oscillators model by employing the lyapunov function method combined with kirchhoff s matrix tree theorem in graph theory we establish a sufficient criterion to guarantee the existence of a stationary distribution for stochastic coupled oscillators moreover a numerical example is given to illustrate the effectiveness of our theoretical results

a note on global stability of the virose equilibrium for network based computer viruses epidemics abstract it has been recently conjectured in yang et al 2013 27 that the unique virose equilibrium of a network based model is globally asymptotically stable in the feasible region the aim of this paper is to investigate the global stability of the virose equilibrium by using the direct lyapunov method and appropriate grouping techniques for lyapunov function derivatives some sufficient conditions are established which improves the relevant results moreover we provide a new brief proof for global stability of the virus free equilibrium by using comparison method and discuss quantitatively the effect of various immunization schemes including uniform immunization targeted immunization and high risk immunization on the viruses spread which suggests promising strategy to halt viruses spread in computer networks

global exponential stability for stochastic coupled systems on networks with markovian switching abstract this paper investigates the global exponential stability of stochastic coupled systems on networks with markovian switching scsnms sufficient conditions are established to guarantee p th moment exponential stability and almost surely exponential stability of the scsnms by using concepts from graph theory and m matrix into lyapunov method consequently the upper boundaries of the p th moment lyapunov exponent and the sample lyapunov exponent are given finally to illustrate the capabilities of the stability principle easy verifiable sufficient conditions of global exponential stability for a stochastic coupled oscillator on network with markovian switching are obtained

hopf pitchfork singularities in coupled systems it is known from the literature that a family consisting of two brusselators linearly coupled by diffusion unfolds strange attractors due to the generic occurrence of a 4 dimensional nilpotent singularity of codimension 4 in this paper the attention is placed on the hopf pitchfork singularities which are unfolded by that coupled system we will see that the associated map of bifurcations is very rich and includes configurations which could also play the role of organizing centers of chaotic dynamics as it happens in the case of two brusselators the occurrence of hopf pitchfork singularities is expected when hopf bifurcations are coupled by a diffusion mechanism on the other hand one of the most interesting problems in the context of coupled systems is the understanding of processes of synchronization desynchronization we will also illustrate the role of hopf pitchfork singularities as organizing centers of these processes

lmi conditions for global stability of fractional order neural networks fractional order neural networks play a vital role in modeling the information processing of neuronal interactions it is still an open and necessary topic for fractional order neural networks to investigate their global stability this paper proposes some simplified linear matrix inequality lmi stability conditions for fractional order linear and nonlinear systems then the global stability analysis of fractional order neural networks employs the results from the obtained lmi conditions in the lmi form the obtained results include the existence and uniqueness of equilibrium point and its global stability which simplify and extend some previous work on the stability analysis of the fractional order neural networks moreover a generalized projective synchronization method between such neural systems is given along with its corresponding lmi condition finally two numerical examples are provided to illustrate the effectiveness of the established lmi conditions

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

global stability of an sir model with differential infectivity on complex networks abstract in this paper an sir model with birth and death on complex networks is analyzed where infected individuals are divided into m groups according to their infection and contact between human is treated as a scale free social network we obtain the basic reproduction number r 0 as well as the effects of various immunization schemes the results indicate that the disease free equilibrium is locally and globally asymptotically stable in some conditions otherwise disease free equilibrium is unstable and exists an unique endemic equilibrium that is globally asymptotically stable our theoretical results are confirmed by numerical simulations and a promising way for infectious diseases control is suggested

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

analysis of a stochastic logistic model with diffusion stochastic logistic model with diffusion and levy jumps is proposed critical value between stability and extinction for species in each patch is obtained critical value has a close relationship with levy jumps numerical simulations are introduced to validate the results taking both white noise and levy jump noise into account a stochastic logistic model with diffusion is proposed and considered under some simple assumptions the almost complete parameters analysis of the model is carried out in each case it is shown that the population in each patch is either stable in time average or extinct depending on the parameters of the model especially depending on the intensity of the levy jump noise some simulation figures are introduced to validate the theoretical results

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

analysis of autonomous lotka volterra competition systems with random perturbation abstract this paper discusses a randomized n species lotka volterra competition system we show that this system is stable in time average under certain conditions furthermore there is a stationary distribution of this system if extra conditions are satisfied also we give the extinction condition of this system finally numerical simulations are carried out to support our results

coupling leads to chaos abstract the main goal of this paper is to prove analytically the existence of strange attractors in a family of vector fields consisting of two brusselators linearly coupled by diffusion we will show that such a family contains a generic unfolding of a 4 dimensional nilpotent singularity of codimension 4 on the other hand we will prove that in any generic unfolding x of an n dimensional nilpotent singularity of codimension n there are bifurcation curves of n 1 dimensional nilpotent singularities of codimension n 1 which are in turn generically unfolded by x arguments conclude recalling that any generic unfolding of the 3 dimensional nilpotent singularity of codimension 3 exhibits strange attractors

local and global behavior near homoclinic orbits we study the local behavior of systems near homoclinic orbits to stationary points of saddle focus type we explicitly describe how a periodic orbit approaches homoclinicity and with the help of numerical examples discuss how these results relate to global patterns of bifurcations

global nonfragile synchronization in finite time for fractional order discontinuous neural networks with nonlinear growth activations this paper is concerned with the global nonfragile mittag leffler synchronization and the global synchronization in finite time for fractional order discontinuous neural networks where activation functions are discontinuous at 0 or modeled as a local holder functions with the nonlinear growth property in a neighborhood of 0 first two lemmas concerned with the convergence with respect to an absolutely continuous function are developed second a new property which introduces an inequality of the fractional derivative for the variable upper limit integral with respect to the nonsmooth integrable function is presented and applied in the synchronization results analysis in addition under the fractional filippov differential inclusion framework by utilizing the lur e postnikov type lyapunov functional nonsmooth analysis method and the convergence properties developed in this paper the synchronization conditions are derived in the form of linear matrix inequalities moreover the upper bound of the setting time for the global nonfragile synchronization in finite time is calculated accurately finally two illustrations are presented to verify the correctness of the theoretical results

global stability of a multi group sei model in this paper a multi group sei model with the bilinear incidence and variable susceptibility and infectivity is analyzed the susceptible individuals are divided into n groups according to their susceptibility and infected individuals are divided into m groups according to infectivities each group of infected individuals has an exposed period the basic reproduction number r 0 is obtained and globally asymptotic stability of disease free equilibrium is proved if r 0 1 the disease free equilibrium is unstable and the endemic equilibrium exists and is unique which is globally asymptotically stable finally some numerical examples are given to illustrate the above analysis

a remark on stochastic logistic model with diffusion stochastic logistic system with diffusion is proposed and studied almost sufficient and necessary conditions for stability in time average and extinction are established some numerical examples are introduced to support the main results

exponential stability of fractional order complex multi links networks with aperiodically intermittent control in this article the exponential stability problem for fractional order complex multi links networks with aperiodically intermittent control is considered using the graph theory and lyapunov method two theorems including a lyapunov type theorem and a coefficient type theorem are given to ensure the exponential stability of the underlying networks the theoretical results show that the exponential convergence rate is dependent on the control gain and the order of fractional derivative to be specific the larger control gain the higher the exponential convergence rate meanwhile when aperiodically intermittent control degenerates into periodically intermittent control a corollary is also provided to ensure the exponential stability of the underlying networks furthermore to show the practicality of theoretical results as an application the exponential stability of fractional order multi links competitive neural networks with aperiodically intermittent control is investigated and a stability criterion is established finally the effectiveness and feasibility of the theoretical results are demonstrated through a numerical example

stability analysis of stochastic delayed complex networks with multi weights based on razumikhin technique and graph theory abstract in this paper a novel kind of stochastic delayed complex networks with multi weights sdcnmw is considered we first split sdcnmw into multiple stochastic complex networks with single weight this paper is mainly concerned with the issues of exponential stability for sdcnmw a global lyapunov functional is constructed by a graph theoretical approach based on kirchhoff s matrix tree theorem razumikhin type theorem is presented by stochastic stability theory and razumikhin technique an easy verified coefficients type theorem is also given finally theoretical results are illustrated by stochastic oscillators network successfully

global stability analysis of an sir epidemic model with demographics and time delay on networks abstract in this paper a susceptible infected recovery sir epidemic model is governed with demographics and time delay on networks firstly the basic reproduction number r 0 is derived dependent on birth rate death rate recovery rate and transmission rate the disease free equilibrium of the model is stable when r 0 1 and unstable when r 0 1 secondly based on a jacobian matrix calculated along with the disease free equilibrium we find that the system does not occur hopf branch under the disease free equilibrium thirdly the global asymptotic stability of a disease free equilibrium and a unique endemic equilibrium are proved by structuring two lyapunov functions finally numerical simulations are performed to illustrate the analysis results

finite time stabilization of delayed memristive neural networks discontinuous state feedback and adaptive control approach in this paper a general class of delayed memristive neural networks dmnns system described by functional differential equation with discontinuous right hand side is considered under the extended filippov framework we investigate the finite time stabilization problem for dmnns by using the famous finite time stability theorem and the generalized lyapunov functional method to do so we design two classes of novel controllers including discontinuous state feedback controller and discontinuous adaptive controller without assuming the boundedness and monotonicity of the activation functions several sufficient conditions are given to stabilize the states of this class of dmnns in finite time moreover the upper bounds of the settling time for stabilization are estimated finally numerical examples are provided to demonstrate the effectiveness of the developed method and the theoretical results

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

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