Global Asymptotic Stability Of Equilibrium Research Articles

Global dynamics of difference equations for SIR epidemic models with a class of nonlinear incidence rates

In this paper, by applying a variation of the backward Euler method, we propose a discrete-time SIR epidemic model whose discretization scheme preserves the global asymptotic stability of equilibria for a class of corresponding continuous-time SIR epidemic models. Using discrete-time analogue of Lyapunov functionals, the global asymptotic stability of the equilibria is fully determined by the basic reproduction number , when the infection incidence rate has a suitable monotone property.

Global stability analysis with a discretization approach for an age-structured multigroup SIR epidemic model

For an age-structured SIR epidemic model, which is described by a system of partial differential equations, the global asymptotic stability of an endemic equilibrium in the situation where the basic reproduction number R 0 is greater than unity has been an open problem for decades. In the present paper, we construct a multigroup epidemic model regarded as a generalization of the model, and study the global asymptotic stability of each of its equilibria. By discretizing the multigroup model with respect to the age variable under some parameter assumptions, we first rewrite the PDE system into an ODE system, and then, applying the classical method of Lyapunov functions and a recently developed graph-theoretic approach with an original idea of maximum value functions, we prove that the global asymptotic stability of each equilibrium of the discretized system is completely determined by R 0 , namely, the disease-free equilibrium is globally asymptotically stable if R 0 ≤ 1 , while an endemic equilibrium exists uniquely and is globally asymptotically stable if R 0 > 1 . A numerical example illustrates that a numerical solution of R 0 for the discretized ODE system becomes closer to that for the original PDE system as the step size of the discretization decreases.

New results on the global asymptotic stability of a Lotka-Volterra system

In this paper, we revisit the famous Lotka-Volterra competitive system. By combining spectral matrix theory with Lyapunov function, some new sufficient conditions are obtained to guarantee the global asymptotic stability of a unique equilibrium for Lotka-Volterra competitive system. Our new results generalize and significantly improve the known results in the previous literature. The main purpose of this paper is to propose a new methodology to study the high-dimensional Lotka-Volterra system. And this method can be extensively used to study the global asymptotic stability of the equilibrium. Finally, some examples and their simulations show the feasibility and effectiveness of our results.

Global asymptotical stability of continuous-time delayed neural networks without global Lipschitz activation functions

This paper investigates the global asymptotic stability of equilibrium for a class of continuous-time neural networks with delays. Based on suitable Lyapunov functionals and the homeomorphism theory, some sufficient conditions for the existence and uniqueness of the equilibrium point are derived. These results extend the previously works without assuming boundedness and Lipschitz conditions of the activation functions and any symmetry of interconnections. A numerical example is also given to show the improvements of the paper.

Stability Results for a Class of Differential Equation and Application in Medicine

AChemostatsystem incorporating hepatocellular carcinomas is discussed. The model generalizes the classicalChemostatmodel, and it assumes that theChemostatis an increasing function of the concentration. The asymptotic behavior of solutions is determined. Sufficient conditions for the local and global asymptotic stability of equilibrium and numerical simulation are obtained, which is used to select the disease control tactics.

Global Asymptotic Stability of Equilibria in Models for Virus Dynamics

In this paper several models in virus dynamics with and without immune response are discussed concerning asymptotic behaviour. The case of immobile cells but diffusing viruses and T-cells is included. It is shown that, depending on the value of the basic reproductive number R0 of the virus, the corresponding equilibrium is globally asymptotically stable. If R0 < 1 then the virus-free equilibrium has this property, and in case R0 > 1 there is a unique disease equilibrium which takes over this property.

A new stability criterion for bidirectional associative memory neural networks of neutral-type

In the paper, the global asymptotic stability of equilibrium is considered for continuous bidirectional associative memory (BAM) neural networks of neutral type by using the Lyapunov method. A new stability criterion is derived in terms of linear matrix inequality (LMI) to ascertain the global asymptotic stability of the BAM. The LMI can be solved easily by various convex optimization algorithms. A numerical example is illustrated to verify our result.

STABILITY OF EQUILIBRIA OF NEURAL NETWORKS

Sufficient conditions for local and global asymptotic stability of equilibria of some general classes of neural networks are presented. In the event that the interconnection matrix is block diagonally stable it is shown that the equilibrium is globally asymptotically stable if the cells are dissipative at the equilibrium. For a special class of networks the conditions of dissipativity are reduced to more readily-tested conditions of passivity. Equilibria are shown to be asymptotically stable essentially if the cells are locally passive.

Global asymptotic stability of non-negative steady states in, model ecosystems—I†

Using a novel modification of a familiar transformation used in Lotka-Volterra systems, global asymptotic stability of equilibria on the boundary of the state space of ecosystems is studied. By means of a natural Lyapunov function, easily verifiable sufficient conditions are obtained for global asymptotic stability of boundary equilibria.

Some conditions for global asymptotic stability of equilibria of integrodifferential equations

Some conditions for global asymptotic stability of equilibria of integrodifferential equations

On Volterra’s Population Equation

On Volterra’s Population Equation