Convergence in Lotka-volterra Type Diffusive Delay Systems without Dominating Instantaneous Negative Feedbacks
نویسندگان
چکیده
This paper deals with the convergence aspect of diffusive delay Lotka-Volterra systems with infinite delays. It is well known that such a system has a globally asymptotically stable steady state if the negative feedbacks of the intraspecific competitions are dominant and instantaneous. It is shown here that such a globally asymptotically stable steady state continues to exist even if the instantaneous assumption is removed, provided that solutions of the system are eventually uniformly bounded and the delays involved in the intraspecific competitions are small. This work generalises several recent related ones.
منابع مشابه
Convergence in Lotka-Volterra-type delay systems without instantaneous feedbacks
Synopsis Most of the convergence results appearing so far for delayed Lotka-Volterra-type systems require that undelayed negative feedback dominate both delayed feedback and interspecific interactions. Such a requirement is rarely met in real systems. In this paper we present convergence criteria for systems without instantaneous feedback. Roughly, our results suggest that in a Lotka-Volterra-t...
متن کاملGlobal Asymptotic Stability in a Nonautonomous n-Species Lotka^Volterra Predator^Prey System with Infinite Delays
In this paper, a delayed n-species nonautonomous Lotka–Volterra type food-chain system without dominating instantaneous negative feedback is investigated. By means of a Lyapunov functional, sufficient conditions are derived for the global asymptotic stability of the positive solution of the system. As a corollary, it is shown that the global asymptotic stability of the positive solution is main...
متن کاملGlobal attractivity of positive periodic solution to periodic Lotka – Volterra competition systems with pure delay ✩
We consider a periodic Lotka–Volterra competition system without instantaneous negative feedbacks (i.e., pure-delay systems) ẋi (t)= xi(t) [ ri (t)− n ∑ j=1 aij (t)xj ( t − τij (t) )] , i = 1,2, . . . , n. (∗) We establish some 3/2-type criteria for global attractivity of a positive periodic solution of the system, which generalize the well-known Wright’s 3/2 criteria for the autonomous delay l...
متن کاملTraveling wavefronts in diffusive and cooperative Lotka – Volterra system with delays ✩
Existence of traveling wave front solutions is established for diffusive and cooperative Lotka–Volterra system with delays. The result is an extension of an existing result for delayed logistic scaler equation to systems, and is somewhat parallel to the existing result for diffusive and competitive Lotka–Volterra systems without delay. The approach used in this paper is the upper–lower solution...
متن کاملAge-dependent diffusive Lotka-Volterra type systems
In this paper it is shown that the sub-supersolution method works for age-dependent diffusive nonlinear systems with non-local initial conditions. As application, we prove the existence and uniqueness of positive solution for a kind of Lotka-Volterra systems, as well as the blow-up in finite time in a particular case.
متن کامل