Periodic Lotka-Volterra competition equations.

2n Positive Periodic Solutions to n Species Non-autonomous Lotka-Volterra Competition Systems with Harvesting Terms

By using Mawhin’s continuation theorem of coincidence degree theory, we establish the existence of 2 positive periodic solutions for n species non-autonomous Lotka-Volterra competition systems with harvesting terms. An example is given to illustrate the effectiveness of our results. Keywords—Positive periodic solutions; Lotka-Volterra competition system; Coincidence degree; Harvesting term.

Soochow Journal of Mathematics

In recent years, non-autonomous delay differential equations have been used in the study of population dynamics, ecology and epidemic. Among those equations, a famous model for population is the Lotka-Volterra competition system. Due to the various seasonal effects present in real life situation, it is reasonable and practical to study the Lotka-Volterra competition system with periodic coeffic...

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

Global 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...

THE QUALITATIVE ANALYSIS OF iv-SPECIES LOTKA-VOLTERRA PERIODIC COMPETITION SYSTEMS

In this paper, we consider an n-species Lotka-Volterra periodic competition system. Using a comparison method and the Brouwer fixed point theorem, we obtain some sufficient conditions for the ultimate boundedness of solutions and the existence and global attractivity of a positive periodic solution. We also point out that these results constitute a generalization of K. Gopalsamy and J. M. Cushi...

Existence and Global Asymptotic Stability of Positive Periodic Solutions of a Lotka-volterra Type Competition Systems with Delays and Feedback Controls

The existence of positive periodic solutions of a periodic LotkaVolterra type competition system with delays and feedback controls is studied by applying the continuation theorem of coincidence degree theory. By contracting a suitable Liapunov functional, a set of sufficient conditions for the global asymptotic stability of the positive periodic solution of the system is given. A counterexample...