相关论文: Persistence, permanence and global stability for a…
The paper concerns a class of $n$-dimensional non-autonomous delay differential equations obtained by adding a non-monotone delayed perturbation to a linear homogeneous cooperative system of ordinary differential equations. This family…
We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…
For a family of $n$-dimensional periodic delay differential equations which encompasses a broad set of models used in structured population dynamics, the existence of a positive periodic solution is obtained under very mild conditions. The…
We consider a system of nonlinear partial differential equations that describes an age-structured population living in changing environment on $N$ patches. We prove existence and uniqueness of solution and analyze large time behavior of the…
We consider scalar delay differential equations $x'(t) = -\delta x(t) + f(t,x_t) (*)$ with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well known Mackey-Glass type equations,…
We consider a system of nonlinear partial differential equations that describes an age-structured population inhabiting several temporally varying patches. We prove existence and uniqueness of solution and analyze its large-time behavior in…
A general nonautonomous Nicholson equation with multiple pairs of delays in {\it mixed monotone} nonlinear terms is studied. Sufficient conditions for permanence are given, with explicit lower and upper uniform bounds for all positive…
We study the behavior of an infinite system of ordinary differential equations modeling the dynamics of a metapopulation, a set of (discrete) populations subject to local catastrophes and connected via migration under a mean field rule; the…
A general reaction-diffusion equation with spatiotemporal delay and homogeneous Dirichlet boundary condition is considered. The existence and stability of positive steady state solutions are proved via studying an equivalent…
For a large family of nonautonomous scalar-delayed differential equations used in population dynamics, some criteria for permanence are given, as well as explicit upper and lower bounds for the asymptotic behavior of solutions. The method…
In this paper, we first give a new definition of almost periodic time scales, two new definitions of almost periodic functions on time scales and investigate some basic properties of them. Then, as an application, by using the fixed point…
The main objective of this paper is a study of the asymptotic behavior of distributional solutions to the one-dimensional repulsive pressureless Euler-Poisson system. The system is a model for the dynamics of a mass distribution evolving on…
We study some aspects of the global dynamics of an $n$-dimensional Lotka-Volterra system with infinite delay and patch structure, such as extinction, persistence, existence and global attractivity of a positive equilibrium. Both the cases…
Using techniques of non-autonomous dynamical systems, we completely characterize the persistence properties of an almost periodic Nicholson system in terms of some numerically computable exponents. Although similar results hold for a class…
In this paper, we consider the diffusive Nicholson's blowflies model in spatially heterogeneous environment when the diffusion rate is large. We show that the ratio of the average of the maximum per capita egg production rate to that of the…
We analyze a reaction-diffusion system describing the growth of microbial species in a model of flocculation type that arises in biology. Existence of global classical positive solutions is proved under general growth assumptions, with…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
In this paper, a stochastic Gilpin-Ayala population model with regime switching and white noise is considered. All parameters are influenced by stochastic perturbations. The existence of global positive solution, asymptotic stability in…
We study the stability and synchronization of predator-prey populations subjected to noise. The system is described by patches of local populations coupled by migration and predation over a neighborhood. When a single patch is considered,…
This article is concerned with a mutualism ecological model with stochastic perturbations. the local existence and uniqueness of a positive solution are obtained with positive initial value, and the asymptotic behavior to the problem is…