Existence of at Least Two Periodic Solutions for a Competition System of Plankton Allelopathy on Time Scales

Abstract

We study a competition system of the growth of two species of plankton with competitive and allelopathic effects on each other on time scales. With the help of Mawhin’s continuation theorem of coincidence degree theory, a set of easily verifiable criteria is obtained for the existence of at least two periodic solutions for this model. Some new existence results are obtained. An example and numerical simulation are given to illustrate the validity of our results.