相关论文: Global asymptotic stability for Gurtin-MacCamy's p…

We analyse the asymptotic behaviour of integro-differential equations modelling $N$ populations in interaction, all structured by different traits. Interactions are modelled by non-local terms involving linear combinations of the total…

This paper is concerned with establishing global asymptotic stability results for a class of non-linear PDE which have some similarity to the PDE of the Lifschitz-Slyozov-Wagner model. The method of proof does not involve a Lyapounov…

In this article, we introduce Lyapunov-type results to investigate the stability of the trivial solution of a Stieltjes dynamical system. We utilize prolongation results to establish the global existence of the maximal solution. Using…

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…

The principle of linearized stability is established for age-structured diffusive populations incorporating nonlinear death and birth processes. More precisely, asymptotic exponential stability is shown for equilibria for which the…

We prove global stability for a system of nonlinear wave equations satisfying a generalized null condition. The generalized null condition allows for null forms whose coefficients have bounded $C^k$ norms. We prove both pointwise decay and…

In this paper, we'll show the robustness of global stability for perturbed dissipative dynamical systems.

A diffusive Lotka-Volterra competition model is considered for the combined effect of spatial dispersal and spatial variations of resource on the population persistence and exclusion. First it is shown that in a two-species system in which…

We consider a generalized alpha-type model in the whole three-dimensional space and driven by a stationary (time-independent) external force. This model contains as particular cases some relevant equations of the fluid dynamics, among them…

In this paper we consider the global stability of solutions of a nonlinear stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…

We study here the dynamics (and stability) of Probabilistic Population Protocols, via the differential equations approach. We provide a quite general model and we show that it includes the model of Angluin et. al. in the case of very large…

This article proposes a non-autonomous mathematical model with delay for confrontation between two countries, and examines the stability of its equilibrium state. Our criteria for stability take into account the influence of the factor of…

We analyze global stability properties of birhythmicity in a self-sustained system with random excitations. The model is a multi-limit cycles variation of the van der Pol oscillatorintroduced to analyze enzymatic substrate reactions in…

Global dynamics of nonautonomous diffusive Hindmarsh-Rose equations on a three-dimensional bounded domain in neurodynamics is investigated. The existence of a pullback attractor is proved through uniform estimates showing the pullback…

For a Nicholson's blowflies system with patch structure and multiple discrete delays, we analyze several features of the global asymptotic behavior of its solutions. It is shown that if the spectral bound of the community matrix is…

We analyze the characteristics of the global attractor of a type of dissipative nonautonomous dynamical systems in terms of the Sacker and Sell spectrum of its linear part. The model gives rise to a pattern of nonautonomous Hopf bifurcation…

This paper deals with the stability analysis of a mass-spring system subject to friction using Lyapunov-based arguments. As the described system presents a stick-slip phenomenon, the mass may then periodically sticks to the ground. The…

We investigate the global dynamics of a renewal-type epidemic model with variable susceptibility. We show that in this extended model there exists a unique endemic equilibrium and prove that it is globally asymptotically stable when $R_0 >…

In "chemostat"-type population models that incorporate substrate (nutrient) dynamics, the dependence of the birth (or growth) rate on the substrate concentration introduces nonlinear coupling that creates a challenge for stabilization that…

We consider a class of physiologically structured population models, a first order nonlinear partial differential equation equipped with a nonlocal boundary condition, with a constant external inflow of individuals. We prove that the…