Global positive periodic solutions of periodic n-species competition systems

Existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems with several deviating arguments.

In this paper, we study the existence and global attractivity of positive periodic solutions of periodic n-species Lotka-Volterra competition systems. By using the method of coincidence degree and Lyapunov functional, a set of easily verifiable sufficient conditions are derived for the existence of at least one strictly positive (componentwise) periodic solution of periodic n-species Lotka-Volt...

Existence of Positive Periodic Solutions for a Class of n-Species Competition Systems with Impulses

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.

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...

n-Species Competition in a Periodic Chemostat

A threshold result on the global dynamics of the scalar asymptotically periodic Kolmogorov equation is proved and then applied to models of single species growth and n-species competition in a periodically operated chemo-stat. The operating parameters and the species speciic response functions can be periodic functions of time. Species speciic removal rates are also permitted. Suucient conditio...