GLOBAL ASYMPTOTIC STABILITY IN N-SPECIES NONAUTONOMOUS LOTKA-VOLTERRACOMPETITIVE SYSTEMS WITH DELAYS

A delayed n-species nonautonomous Lotka-Volterra type competitive system without dominating instantaneous negative feedback is investigated. By means of a suitable Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solutions of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is maintained provided that the delayed negative feedbacks dominate other interspecific interaction effects with delays and the delays are sufficiently small.

GLOBAL ASYMPTOTIC STABILITY FOR A NONLINEAR DELAY DIFFERENCE EQUATION

In this paper,a sufficient condition for the global asymptotic stability of the solutions of the following nonlinear delay difference equation is obtained, xn+ 1=xn+xn- 1xn- 2 +a xnxn- 1+xn- 2 +a, n =0 ,1 ,..., where a∈ [0 ,∞ ) and the initial values x- 2 ,x- 1,x0 ∈ (0 ,∞ ) .As a special case,a conjecture by Ladas is confirmed.

LMI-based approach for global asymptotic stability analysis of continuous BAM neural networks

Studies on the stability of the equilibrium points of continuous bidirectional associative memory (BAM) neural network have yielded many useful results. A novel neural network model called standard neural network model (SNNM) is ad- vanced. By using state affine transformation, the BAM neural networks were converted to SNNMs. Some sufficient conditions for the global asymptotic stability of continuous BAM neural networks were derived from studies on the SNNMs’ stability. These conditions were formulated as easily verifiable linear matrix inequalities (LMIs), whose conservativeness is relatively low. The approach proposed extends the known stability results, and can also be applied to other forms of recurrent neural networks (RNNs).

Global asymptotic stability for Hopfield-type neural networks with diffusion effects

The existence, uniqueness and global asymptotic stability for the equilibrium of Hopfield-type neural networks with diffusion effects are studied. When the activation functions are monotonously nondecreasing, differentiable, and the interconnected matrix is related to the Lyapunov diagonal stable matrix, the sufficient conditions guaranteeing the existence of the equilibrium of the system are obtained by applying the topological degree theory. By means of constructing the suitable average Lyapunov functions, the global asymptotic stability of the equilibrium of the system is also investigated. It is shown that the equilibrium （if it exists） is globally asymptotically stable and this implies that the equilibrium of the system is unique.

New Delay-dependent Global Asymptotic Stability Condition for Hopfield Neural Networks with Time-varying Delays

This paper deals with the global asymptotic stability problem for Hopfield neural networks with time-varying delays. By resorting to the integral inequality and constructing a Lyapunov-Krasovskii functional, a novel delay-dependent condition is established to guarantee the existence and global asymptotic stability of the unique equilibrium point for a given delayed Hopfield neural network. This criterion is expressed in terms of linear matrix inequalities （LMIs）, which can be easily checked by utilizing the recently developed algorithms for solving LMIs. Examples are provided to demonstrate the effectiveness and reduced conservatism of the proposed condition.

Global Asymptotic Stability of Zero Solution for Delay Difference Equations

The difference equation △xn＋ pnxn-k = f（n,xn-1,...,xn-1m）, n = 0, 1,2,.. is considered, where {pn} is a sequence of nonnegative real numbers, m ∈ {1, 2, ,... }, k,l1,..., lm ∈ {0, 1, 2,,... }. Some sufficient conditions for the global asymptotic stability of zero solution of the equation are obtained.

Global Asymptotic Stability for a Class of Nonlinear Populations Model

This paper discussed the stability of model of an age structured population systems,proved that the equilibrium solution systems is globally asymptotically stable.

Global Asymptotic Stability of a Kind of Stochastic SIRS Model

A detailed analysis was carried out on global asymptotic behavior of a kind of stochastic SIRS(susceptible-infective-removed-susceptible)model.This model has been obtained by introducing stochasticity into the original deterministic SIRS model via the technique of parameter perturbation which is standard in stochastic population modeling.By making corresponding Lyapunov function and using It formula,the condition for the solution of the model tending to the disease free equilibrium asymptotically was obtained.Under this condition,the epidemics will die out as time goes by.Based on this,almost surely exponential stability was analyzed.

Lyapunov functions for studying global asymptotic stability of two rumor spreading models

In a previous work(2018,Commun.Theor.Phys.70,795–802),a new compartment model for the spreading of rumors was introduced and analyzed.However,only the local asymptotic stability of this model was discussed.In the present work,we first provide a rigorous mathematical analysis for the global asymptotic stability(GAS)of the above-mentioned rumor spreading model.By constructing suitable Lyapunov candidate functions,we obtain the GAS of a rumor-free(boundary)equilibrium point and a unique rumor-spreading(positive)equilibrium point.After that,we utilize the approach based on the Lyapunov candidate functions to study the GAS of another rumor spreading model with control strategies,which was proposed in(2022,Physica A 606,128157).As an important consequence,the GAS of the rumor spreading model with control strategies is determined fully without resorting to technical hypotheses used in the benchmark work.Lastly,the theoretical findings are supported by a set of illustrative numerical examples.The obtained results not only improve the ones constructed in the two abovementioned benchmark papers but also can be extended to study the global dynamics of other rumor propagation models in the context of both integer-order and fractional-order derivatives.

GLOBAL ASYMPTOTIC STABILITY OF THE PERIODIC LOTKA－VOLTERRA SYSTEM WITH TWO－PREDATORS AND ONE－PREY

The three species Lotka-Volterra periodic model with two predators and one prey is considered.A set of easily verifiable sufficient conditions is obtained.Finallyt an example is given to illustrate the feasibility of these conditions.

PERIODIC SOLUTIONS AND GLOBAL ASYMPTOTIC STABILITY OF A DELAYED DISCRETE PREDATOR-PREY SYSTEM WITH HOLLING II TYPE FUNCTIONAL RESPONSE

In this paper, we study the existence and global asymptotic stability of positive periodic solutions of a delayed periodic predator-prey system with Hoffing Ⅱ type functional response. By use of the continuation theorem of coincidence degree theory and the method of Lyapunov function, some sufficient conditions are obtained.

Stability of second order Hopfield neural networks with time delays

Dynamical behaviors of a class of second order Hopfield neural networks with time delays is investigated.The existence of a unique equilibrium point is proved by using Brouwer's fixed point theorem and the counter proof method,and some sufficient conditions for the global asymptotic stability of the equilibrium point are obtained through the combination of a suitable Lyapunov function and an algebraic inequality technique.

BOUNDEDNESS AND PERSISTENCE AND GLOBAL ASYMPTOTIC STABILITY FOR A CLASS OF DELAY DIFFERENCE EQUATIONS WITH HIGHER ORDER

Some sufficient, conditions for boundedness and persistence and global asymptotic stability of solutions for a class of delay difference equations with higher order are obtained, which partly solve G. Ladas' two open problems and extend some known results.

Global asymptotical stability in a rational difference equation

In this paper we prove a global attractivity result for the unique positive equilibrium point of a difference equation,which improves and generalizes some known ones in the existing literature.Especially,our results completely solve an open problem and some conjectures proposed in[1,2,3,4].

Global asymptotic stability for a SEI reaction-diffusion model of infectious diseases with immigration

This paper studies the local and global stability of solutions for a spatially spread SEI epidemic model with immigration of individuals using a Lyapunov functional. It is shown that in the presence of diffusion, the unique steady state remains globally stable. Numerical results obtained through Matlab simulations are presented to confirm the findings of this study.

Globally Asymptotic Stability of Equilibrium of a Dynamical Model with Infinite Delay

By using a criterion for asymptotic stability in Banach space BC, a group of sufficient condi-tioas for a dynamical model with infinite delay which is derived from hematology were obtained, which refined the result in the reference [ 10] got by the second author herself.

GLOBAL ASYMPTOTIC STABILITY IN NONAUTONOMOUS LOTKA-VOLTERRA COMPETITIVE SYSTEM WITH INFINITE DELAY AND FEEDBACK CONTROLS

In this paper, we study a nonautonomous Lotka-Volterra competitive system with infnite delay and feedback controls. By means of a suitable Lyapunov functional, we establish sufcient conditions which guarantee the global asymptotic stability of the system.

GLOBAL STABILITY OF AN SIRS EPIDEMIC MODEL WITH DELAYS

In this article, an SIRS epidemic model spread by vectors （mosquitoes） which have an incubation time to become infectious is formulated. It is shown that a disease-free equilibrium point is globally stable if no endemic equilibrium point exists. Further, the endemic equilibrium point （if it exists） is globally stable with a respect ＂weak delay＂. Some known results are generalized.

PERSISTENCE AND GLOBAL STABILITY FOR A THREE-SPECIES RATIO-DEPENDENT PREDATOR-PREY SYSTEM WITH TIME DELAYS IN TWO-PATCH ENVIRONMENTS

A three-species ratio-dependent predator-prey diffusion model with time delays is investigated. It is shown that the system is uniformly persistent under some appropriate conditions, and sufficient conditions axe obtained for the global stability of the positive equilibrium of the system.

GLOBAL STABILITY OF EXTENDED MULTI-GROUP SIR EPIDEMIC MODELS WITH PATCHES THROUGH MIGRATION AND CROSS PATCH INFECTION

In this article, we establish the global stability of an endemic equilibrium of multi-group SIR epidemic models, which have not only an exchange of individuals between patches through migration but also cross patch infection between different groups. As a result, we partially generalize the recent result in the article [16].