With A Harvest Rate Of Multiple Positive Periodic Solutions Of The Lotka-volterra Diffusion Systems

In this paper, we study a class of delay Lotka-Volterra competition diffusive systems and ratio-dependent predator-prey diffusive systems of two species with harvesting. A set of easily verifiable sufficient conditions are obtained for the existence ,of multiple positive periodic solutions for these two models. The approach is based on Mawhin's continuation theorem of coincidence degree theory as well as some priori estimates. This is the first time that delay Lotka-Volterra diffusive systems of two species with harvesting have been studied by using this method.The whole paper consists of three chapters. In Chapter 1, we introduce some elementary concepts and results from coincidence degree theory. In Chapter 2, we consider a class of delay Lotka-Volterra competition diffusive systems with harvesting. By applying Mawhin's continuation theorem of coincidence degree theory, we establish a set of suffficient conditions under which this system has at least two positive periodic solutions. In Chapter 3, we consider a class of ratio-dependent predator-prey diffusive systems of two species with harvesting. By applying Mawhin's continuation theorem of coincidence degree theory, we establish a set of suffficient conditions under which this system has at least four positive periodic solutions.