A discrete periodic lotka-volterra system with delays

A Periodic Lotka-volterra System

In this paper periodic time-dependent Lotka-Volterra systems are considered. It is shown that such a system has positive periodic solutions. It is done without constructive conditions over the period and the parameters. 1. The Periodic Lotka-Volterra System. Consider the Predator-Prey model (see Volterra [1]) N ′ 1 = (ε1 − γ1N2)N1 N ′ 2 = (−ε2 + γ2N1)N2. (1) The functions N1 and N2 measure the ...

Permanence and existence of periodic solution of a discrete periodic Lotka–Volterra competition system with feedback control and time delays∗

Existence of Positive Periodic Solutions of a Lotka-Volterra System with Multiple Time Delays

The research is supported by National Natural Science Foundation of China (No. 10771215) Abstract In this paper, a class of Lotka-Volterra system with multiple time delays is considered. By using the continuation theorem of coincidence degree theory, we derive a set of easily verifiable sufficient conditions that guarantees the existence of at least a positive periodic solution.

Positive almost periodic solutions for a predator-prey Lotka-Volterra system with delays

In this paper, by using Mawhin's continuation theorem of coincidence degree theory, sufficient conditions for the existence of positive almost periodic solutions are obtained for the predator-prey Lotka-Volterra competition system with delays        du i (t) dt = u i (t) a i (t) − n l=1 a il (t)u l (t − σ il (t)) − m j=1 b ij (t)v j (t − τ ij (t)) dv j (t) dt = v j (t) − r j (t) + n l=1 ...

Four Positive Periodic Solutions of a Discrete Time Lotka-volterra Competitive System with Harvesting Terms

In this paper, by using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.