performance analysis of an adaptive notch filter with constrained poles and zeros a statistical analysis of the sine wave frequency estimate obtained by the adaptive notch filter anf recently proposed by a nehorai ibid vol assp 33 p 983 96 aug 1985 is presented asymptotically valid expressions for the bias and mean square error of the frequency estimate are provided the analysis verifies the performance exhibited by the anf and clarifies the role of some user variables such as the notch bandwidth and the number of data samples processed

stochastic characteristics of a chemostat model with variable yield abstract in this paper a stochastic chemostat model with variable yield is investigated the environment noises are given by independent standard brownian motions and the yield coefficient reflecting the conversion of nutrient to microorganism varies depending on the ambient nutrient first we give that the stochastic system has a unique global positive solution second the sufficient conditions for the extinction and strong persistence in the mean of the microorganism are established third by using stochastic lyapunov function the existence of a unique stationary distribution to the stochastic model is studied in addition some numerical simulations are carried to illustrate the theoretical results and the influence of the variable yield on the microorganism

stationary distribution of a stochastic delayed sveir epidemic model with vaccination and saturation incidence abstract in this paper we develop and analyze a stochastic delayed sveir epidemic model with vaccination and saturation incidence by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model the existence of a stationary distribution implies stochastic weak stability numerical simulations are introduced to illustrate the analytical result

periodic solution for the stochastic chemostat with general response function abstract this paper addresses a stochastic chemostat model with periodic dilution rate and general class of response functions the general functional response is assumed to satisfy two classifications of conditions and these assumptions on the functional response are relative weak that are valid for many forms of growth response for the chemostat with periodic dilution rate we derive the sufficient criteria for the existence of the stochastic nontrivial positive periodic solution by utilizing khasminskii s theory on periodic markov process

extinction and stationary distribution of a stochastic sirs epidemic model with standard incidence rate and partial immunity abstract in this paper a stochastic sirs model with standard incidence rate and partial temporary immunity is proposed the sufficient conditions of the extinction and the existence of a stationary probability measure for the disease are established our results reveal that random perturbations in the environment can restrain the spread of disease that is the deterministic model neglecting random perturbations overestimates the ability of the disease to spread the numerical simulations are carried out to demonstrate the analytical results

analysis of stochastic multimolecular biochemical reaction model with levy jumps abstract in this paper a stochastic multimolecular biochemical reaction model with levy jumps is investigated firstly we prove the existence and uniqueness of the global positive solution then we derive the conditions when the reaction will end and when the reaction will proceed moreover the existence of positive recurrence to the solutions is studied by constructing suitable lyapunov functions results show that the end and persistence of the reaction are closely related to the intensity of levy noise finally numerical simulations are carried out to illustrate the theoretical results

analysis of a deterministic and a stochastic epidemic model with two distinct epidemics hypothesis abstract in this paper we discuss an epidemic model with double hypothesis combined two different transmission mechanisms first we prove the local asymptotic stability of the equilibrium solutions of deterministic system moreover we establish the global stability for the free equilibrium second we show for stochastic system the extinction and persistence in mean of the disease under some conditions on parameters of the model finally numerical simulations are used to confirm our analytical results

stationary distribution and extinction of a stochastic predator prey model with additional food and nonlinear perturbation abstract in this paper we formulate and analyze a stochastic predator prey model with additional food and nonlinear perturbation firstly by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence of an ergodic stationary distribution of the positive solution to the model then we obtain sufficient conditions for extinction of the predator species in two cases one is the prey species surviving and the predator species extinction the other is both the prey and predator species are extinct finally some examples together with numerical simulations are provided to illustrate the analytical results

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

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

threshold behavior of a stochastic lotka volterra food chain chemostat model with jumps abstract taking levy jumps into account a lotka volterra food chain chemostat model in random environment is proposed and investigated we first prove the existence and uniqueness of the global positive solution then conditions for extinction of the microorganisms are derived in two cases furthermore we establish sufficient conditions for persistence in the mean of the system theoretical analysis indicates that the dynamics of the considered model are determined by two threshold parameters r 0 s and r 1 s and both white noise and levy noise are disadvantageous to the system finally numerical simulations are given to illustrate the results

a flexible terminal approach to stochastic stability and stabilization of continuous time semi markovian jump systems with time varying delay abstract this paper addresses the stochastic stability and stabilization problems for a class of semi markovian jump systems smjss with time varying delay where the time varying delay t is assumed to satisfy 1 t 2 based on the flexible terminal approach the time varying delay t is first transformed such that 1 t t 2 t by utilizing a novel semi markovian lyapunov krasoviskii functional smlkf and an improved reciprocally convex inequality rci sufficient conditions are established to guarantee a feasible solution two illustrated examples are shown the effectiveness of the main results

optimal harvesting policy of a stochastic two species competitive model with levy noise in a polluted environment abstract as well known that the sudden environmental shocks and toxicant can affect the population dynamics of fish species a mechanistic understanding of how sudden environmental change and toxicant influence the optimal harvesting policy requires development this paper presents the optimal harvesting of a stochastic two species competitive model with levy noise in a polluted environment where the levy noise is used to describe the sudden climate change due to the discontinuity of the levy noise the classical optimal harvesting methods based on the explicit solution of the corresponding fokker planck equation are invalid the object of this paper is to fill up this gap and establish the optimal harvesting policy by using of aggregation and ergodic methods the approximation of the optimal harvesting effort and maximum expectation of sustainable yields are obtained numerical simulations are carried out to support these theoretical results our analysis shows that the levy noise and the mean stress measure of toxicant in organism may affect the optimal harvesting policy significantly

the dynamics of a stochastic vaccinated tuberculosis model with treatment abstract in this paper we study a stochastic model with vaccination and treatment to describe the transmission dynamics of tuberculosis firstly by using the stochastic lyapunov analysis method we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model then we obtain sufficient conditions for extinction of the diseases our work greatly improves the results of feng and qiu 2018 finally some examples and numerical simulations are introduced to illustrate our theoretical results

dynamics of a stochastic cell to cell hiv 1 model with distributed delay abstract in this paper we consider a stochastic cell to cell hiv 1 model with distributed delay firstly we show that there is a global positive solution of this model before exploring its long time behavior then sufficient conditions for extinction of the disease are established moreover we obtain sufficient conditions for the existence of an ergodic stationary distribution of the model by constructing a suitable stochastic lyapunov function the stationary distribution implies that the disease is persistent in the mean finally we provide some numerical examples to illustrate theoretical results

stochastic analysis of a novel nonautonomous periodic siri epidemic system with random disturbances abstract in this paper a new stochastic nonautonomous siri epidemic model is formulated given that the incidence rates of diseases may change with the environment we propose a novel type of transmission function the main aim of this paper is to obtain the thresholds of the stochastic siri epidemic model to this end we investigate the dynamics of the stochastic system and establish the conditions for extinction and persistence in mean of the disease by constructing some suitable lyapunov functions and using stochastic analysis technique furthermore we show that the stochastic system has at least one nontrivial positive periodic solution finally numerical simulations are introduced to illustrate our results

dynamics of a stochastic lotka volterra model perturbed by white noise abstract this paper continues the study of mao et al investigating two aspects of the equation d x t diag x 1 t x n t b a x t d t x t d w t t 0 the first of these is to slightly improve results in x mao s sabais e renshaw asymptotic behavior of stochastic lotka volterra model j math anal 287 2003 141 156 concerning with the upper growth rate of the total quantity i 1 n x i t of species by weakening hypotheses posed on the coefficients of the equation the second aspect is to investigate the lower growth rate of the positive solutions by using lyapunov function technique and using a changing time method we prove that the total quantity i 1 n x i t always visits any neighborhood of the point 0 and we simultaneously give estimates for this lower growth rate

qualitative analysis of a stochastic epidemic model with specific functional response and temporary immunity abstract in this paper we propose a stochastic delayed epidemic model with specific functional response the time delay represents temporary immunity period i e time from recovery to becoming susceptible again we first show that the proposed model is mathematically and biologically well posed moreover the extinction of the disease and the persistence in the mean are established in the terms of a threshold value r 0 s which is smaller than the basic reproduction number r 0 of the corresponding deterministic system

dynamics of a stochastic predator prey model with distributed delay and markovian switching abstract in this paper we study a stochastic predator prey model with distributed delay and markovian switching firstly we obtain sufficient criteria for weak persistence of the predator population then in the case of weak persistence we establish sufficient conditions for the existence of positive recurrence of the solutions to the model by constructing a suitable stochastic lyapunov function with regime switching finally we establish sufficient conditions for extinction of the predator population

dynamic behaviors of a two group stochastic sirs epidemic model with standard incidence rates abstract this paper deals with a two group stochastic sirs epidemic model with standard incidence rates on one hand we establish sufficient conditions for the existence of a stationary distribution of the positive solutions to the model by constructing a suitable stochastic lyapunov function on the other hand we show the sufficient conditions for the diseases to be extinct

generating series for interconnected analytic nonlinear systems given two analytic nonlinear input output systems represented as fliess operators four system interconnections are considered in a unified setting the parallel connection product connection cascade connection and feedback connection in each case the corresponding generating series is produced and conditions for the convergence of the corresponding fliess operator are given in the process an existing notion of a composition product for formal power series has its set of known properties significantly expanded in addition the notion of a feedback product for formal power series is shown to be well defined in a broad context and its basic properties are characterized

asymptotic behavior of a stochastic delayed hiv 1 infection model with nonlinear incidence abstract in this paper a stochastic delayed hiv 1 infection model with nonlinear incidence is proposed and investigated first of all we prove that there is a unique global positive solution as desired in any population dynamics then by constructing some suitable lyapunov functions we show that if the basic reproduction number r 0 1 then the solution of the stochastic system oscillates around the infection free equilibrium e 0 while if r 0 1 then the solution of the stochastic system fluctuates around the infective equilibrium e sufficient conditions of these results are established finally we give some examples and a series of numerical simulations to illustrate the analytical results

the extinction and persistence of the stochastic sis epidemic model with vaccination abstract in this paper we discuss the dynamics of a stochastic sis epidemic model with vaccination when the noise is large the infective decays exponentially to zero regardless of the magnitude of r 0 when the noise is small sufficient conditions for extinction exponentially and persistence in the mean are established the results are illustrated by computer simulations

stochastic periodic solution for a perturbed non autonomous predator prey model with generalized nonlinear harvesting and impulses abstract in this paper stochastic non autonomous predator prey models with and without impulses are investigated the effects of generalized nonlinear harvesting for prey and predator populations are considered for the stochastic system without impulses the existence and uniqueness of the positive solution is proven and sufficient conditions that guarantee the extinction and persistence of the population in the mean are achieved we show the existence of a nontrivial positive periodic solution by constructing appropriate lyapunov functions and using khasminskii s theory moreover the global attractiveness and stochastic persistence in probability of the stochastic model are discussed results show that the stronger noises and nonlinear harvesting component can significantly influence the dynamics of the system and lead to the extinction of the predator population additionally for the stochastic predator prey system with impulsive effect we prove that there exists a positive periodic solution numerical simulations are conducted to show the effectiveness and feasibility of the obtained results

a stochastic differential equation sis epidemic model in this paper we extend the classical susceptible infected susceptible epidemic model from a deterministic framework to a stochastic one and formulate it as a stochastic differential equation sde for the number of infectious individuals i t we then prove that this sde has a unique global positive solution i t and establish conditions for extinction and persistence of i t we discuss perturbation by stochastic noise in the case of persistence we show the existence of a stationary distribution and derive expressions for its mean and variance the results are illustrated by computer simulations including two examples based on real life diseases

threshold of a regime switching sirs epidemic model with a ratio dependent incidence rate abstract in this paper we study the dynamical behavior of a regime switching sirs epidemic model with a ratio dependent incidence rate we propose a stochastic reproduction number r 0 s which can be regarded as a threshold to use in identifying the stochastic extinction and persistence if r 0 s 1 the disease dies out exponentially with probability one while if r 0 s 1 there exists a unique ergodic stationary distribution of the positive solutions to the system which implies the stochastic persistence of the infectious disease

a stochastic chemostat model with an inhibitor and noise independent of population sizes abstract in this paper a stochastic chemostat model with an inhibitor is considered here the inhibitor is input from an external source and two organisms in chemostat compete for a nutrient firstly we show that the system has a unique global positive solution secondly by constructing some suitable lyapunov functions we investigate that the average in time of the second moment of the solutions of the stochastic model is bounded for a relatively small noise that is the asymptotic behaviors of the stochastic system around the equilibrium points of the deterministic system are studied however the sufficient large noise can make the microorganisms become extinct with probability one although the solutions to the original deterministic model may be persistent finally the obtained analytical results are illustrated by computer simulations

analysis of a novel stochastic sirs epidemic model with two different saturated incidence rates abstract this paper presents a stochastic sirs epidemic model with two different nonlinear incidence rates and double epidemic asymmetrical hypothesis and we devote to develop a mathematical method to obtain the threshold of the stochastic epidemic model we firstly investigate the boundness and extinction of the stochastic system furthermore we use ito s formula the comparison theorem and some new inequalities techniques of stochastic differential systems to discuss persistence in mean of two diseases on three cases the results indicate that stochastic fluctuations can suppress the disease outbreak finally numerical simulations about different noise disturbance coefficients are carried out to illustrate the obtained theoretical results

exponential stability and extended dissipativity criteria for generalized discrete time neural networks with additive time varying delays abstract this paper is concerned with exponential stability and extended dissipativity criteria for generalized discrete time neural networks gdnns with additive time varying delays the generalized dissipativity analysis combines a few previous results into a framework such as l 2 l performance h performance passivity performance strictly q s r dissipative and strictly q s r dissipative the definition of exponential stability for gdnns is given with a new and more appropriate expression a novel augmented lyapunov krasovskii functional lkf which involves more information about the additive time varying delays is constructed by introducing more zero equalities and using a new double summation inequality together with finsler s lemma an improved delay dependent exponential stability and extended dissipativity criterion are derived in terms of convex combination technique cct finally numerical examples are given to illustrate the usefulness and advantages of the proposed methods

periodic solution and ergodic stationary distribution of two stochastic siqs epidemic systems abstract this paper proposes two stochastic siqs epidemic models with periodic parameters and markov switching we first prove that the stochastic non autonomous periodic system has a nontrivial positive periodic solution by using the khasminskii s theory then the sufficient conditions for extinction of the disease are obtained furthermore we construct suitable stochastic lyapunov functions with regime switching to prove the existence of ergodic stationary distribution of the stochastic siqs epidemic model at last some rigorous numerical simulations are presented to illustrate our theoretical results

endemic threshold results for an age structured sis epidemic model with periodic parameters abstract the main contribution of this paper is to obtain a threshold value for the existence and uniqueness of a nontrivial endemic periodic solution of an age structured sis epidemic model with periodic parameters under the assumption of the weak ergodicity of a non autonomous lotka mckendrick system we formulate a normalized system for an infected population as an initial boundary value problem of a partial differential equation the existence problem for endemic periodic solutions is reduced to a fixed point problem of a nonlinear integral operator acting on a banach space of locally integrable periodic l 1 valued functions we prove that the spectral radius of the frechet derivative of the integral operator at zero plays the role of a threshold for the existence and uniqueness of a nontrivial fixed point of the operator corresponding to a nontrivial periodic solution of the original differential equation in a weak sense if the malthusian parameter of the host population is equal to zero our threshold value is equal to the well known epidemiological threshold value the basic reproduction number r 0 however if it is not the case then two threshold values are different from each other and we have to pay attention on their actual biological implications

analysis of a stochastic hiv 1 infection model with degenerate diffusion abstract this paper studies a stochastic hiv 1 infection model with degenerate diffusion the asymptotic dynamics of the stochastic model are shown to be governed by a threshold parameter when the parameter is negative the infection is predicted to go extinct exponentially while the level of healthy cells converges weakly to a unique invariant measure when the threshold parameter is positive the solution of the stochastic model converges polynomially to a unique invariant probability measure indicating that the system admits a unique ergodic stationary distribution numerical simulations are conducted to show the analytical results these results highlight the role of environmental noise in the spread of hiv 1 the method can also be applied to the non degenerate systems

a class of stochastic delayed sir epidemic models with generalized nonlinear incidence rate and temporary immunity abstract a class of sir epidemic model with generalized nonlinear incidence rate is presented in this paper temporary immunity and stochastic perturbation are also considered the existence and uniqueness of the global positive solution is achieved sufficient conditions guaranteeing the extinction and persistence of the epidemic disease are established moreover the threshold behavior is discussed and the threshold value r 0 is obtained we show that if r 0 1 the disease eventually becomes extinct with probability one whereas if r 0 1 then the system remains permanent in the mean

dynamics of a novel nonlinear stochastic sis epidemic model with double epidemic hypothesis abstract in this paper we propose new mathematical models with nonlinear incidence rate and double epidemic hypothesis then we dedicate to develop a method to obtain the threshold of the stochastic sis epidemic model to this end first we investigate the stability of the equilibria of the deterministic system and obtain the conditions for the extinction and the permanence of two epidemic diseases second we explore and obtain the threshold of a stochastic sis system for the extinction and the permanence in mean of two epidemic diseases the results show that a large stochastic disturbance can cause infectious diseases to go to extinction in other words the persistent infectious disease of a deterministic system can become extinct due to the white noise stochastic disturbance this implies that the stochastic disturbance is conducive to epidemic diseases control to illustrate the performance of the theoretical results we present a series of numerical simulations of these cases with respect to different noise disturbance coefficients

a delayed vaccinated epidemic model with nonlinear incidence rate and levy jumps abstract a stochastic susceptible infectious recovered epidemic model with nonlinear incidence rate is formulated to discuss the effects of temporary immunity vaccination and le vy jumps on the transmission of diseases we first determine the existence of a unique global positive solution and a positively invariant set for the stochastic system sufficient conditions for extinction and persistence in the mean of the disease are then achieved by constructing suitable lyapunov functions based on the analysis we conclude that noise intensity and the validity period of vaccination greatly influence the transmission dynamics of the system

optimal control strategy for an impulsive stochastic competition system with time delays and jumps abstract driven by both white and jump noises a stochastic delayed model with two competitive species in a polluted environment is proposed and investigated by using the comparison theorem of stochastic differential equations and limit superior theory sufficient conditions for persistence in mean and extinction of two species are established in addition we obtain that the system is asymptotically stable in distribution by using ergodic method furthermore the optimal harvesting effort and the maximum of expectation of sustainable yield esy are derived from hessian matrix method and optimal harvesting theory of differential equations finally some numerical simulations are provided to illustrate the theoretical results

qualitative study of a stochastic sis epidemic model with vertical transmission abstract in this paper we study a stochastic sis epidemic model with vertical infection by constructing suitable stochastic lyapunov function we establish sufficient conditions for the existence of a stationary probability measure of the model in addition we also establish sufficient conditions for extinction and persistence of the disease

modeling and dynamical analysis of a triple delayed prey predator scavenger system with levy jumps abstract in this paper a hybrid triple delayed prey predator scavenger system with commercial harvesting and levy jumps is established where both maturation delay for prey population and gestation delays for predator and scavenger population are considered for deterministic system positivity and uniform permanence of solution are discussed local stability analysis of deterministic system around interior equilibrium is investigated due to variations of triple time delays for stochastic system without time delay sufficient conditions for stochastically ultimate boundedness and stochastic permanence are discussed for stochastic system with triple time delays existence and uniqueness of global positive solution are studied by constructing appropriate lyapunov functions asymptotic behavior of the hybrid stochastic system with triple time delays and levy jumps is discussed numerical simulations are supported to illustrate theoretical results

modelling a stochastic hiv model with logistic target cell growth and nonlinear immune response function abstract a stochastic hiv viral model with both logistic target cell growth and nonlinear immune response function is formulated to investigate the effect of white noise on each population the existence of the global solution is verified by employing a novel combination of lyapunov functions we obtain the existence of the unique stationary distribution for small white noises we also derive the extinction of the virus for large white noises numerical simulations are performed to highlight the effect of white noises on model dynamic behaviour under the realistic parameters it is found that the small intensities of white noises can keep the irregular blips of hiv virus and ctl immune response while the larger ones force the virus infection and immune response to lose efficacy

dynamical behaviors of a stochastic malaria model a case study for yunnan china abstract in this paper we investigate dynamical behaviors for a stochastic malaria model by introducing the effect of environmental white noise on transmission dynamics of malaria firstly the distance between stochastic solutions and the disease free equilibrium of the corresponding deterministic model is estimated in the time mean sense by constructing stochastic lyapunov functions particularly by the comparison theorem of stochastic differential equations and the law of large numbers sufficient conditions for the extinction of the disease are obtained in the special case next the existence of the unique ergodic stationary distribution is proved by constructing a suitable lyapunov function finally the model is used to simulate the human malaria data in yunnan province and predict the trend of malaria in yunnan

dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth abstract in this paper we investigate the dynamical behavior of a stochastic sei epidemic model with saturation incidence and logistic growth firstly by constructing a suitable stochastic lyapunov function we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the solutions to the model then we obtain sufficient conditions for extinction of the disease in two cases that is the first case is that the susceptible population survival and infected and exposed populations extinction the second case is that all the populations extinction

behavior of a stochastic sir epidemic model with saturated incidence and vaccination rules abstract in this paper the threshold behavior of a susceptible infected recovered sir epidemic model with stochastic perturbation is investigated firstly it is obtained that the system has a unique global positive solution with any positive initial value random effect may lead to disease extinction under a simple condition subsequently sufficient condition for persistence has been established in the mean of the disease finally some numerical simulations are carried out to confirm the analytical results

global analysis and numerical simulations of a novel stochastic eco epidemiological model with time delay abstract in this paper a new stochastic eco epidemiological model is proposed and investigated and the high dimensional model includes time delay and a general incidence rate which make the study more complex first the existence and uniqueness of the global positive solution with any positive initial value are verified second using stochastic analysis methods and some differential inequality techniques we explore the long time asymptotic properties of the stochastic delayed system furthermore we prove that the solution of the stochastic delayed system has a unique stationary distribution and it has ergodic property third the sufficient conditions of permanence in mean or extinction for the ecological populations are obtained finally we introduce a series of computer simulations to show the performance of the theoretical results

stationary distribution of a stochastic within host dengue infection model with immune response and regime switching abstract in this paper we develop a mathematical model of viral infection of monocytes population by dengue virus with immune response which is perturbed by both white and telegraph noises by constructing a suitable stochastic lyapunov function with regime switching we establish sufficient conditions for the existence and uniqueness of an ergodic stationary distribution of the positive solutions to the model the existence of a stationary distribution implies stochastic weak stability

dynamics of a stochastic sis model with double epidemic diseases driven by levy jumps abstract this paper is to investigate the dynamics of a stochastic sis epidemic model with saturated incidence rate and double epidemic diseases which make the research more complex the environment variability in this study is characterized by white noise and jump noise sufficient conditions for the extinction and persistence in the mean of two epidemic diseases are obtained it is shown that the two diseases can coexist under appropriate conditions finally numerical simulations are introduced to illustrate the results developed