Kinetic Studies On The Intrinsic Rate Of Increase Has Disturbed The May-Leonard Model Of The Long-term

This paper is concerned with the dynamical behavior of the May-Leonard modelwith the perturbed intrinsic growth rate. By comparing the phase portraits of theperturbed system with that of the system without the perturbation, we find thepossible relationship between them, which is proved later.The long-time dynamical behavior of the May-Leonard model with sameperiodically perturbed intrinsic growth rate is analyzed, and we give the completeclassification which is similar as that of the autonomous May-Leonard model.The general n-dimensional Lotka-Volterra model with same perturbed intrinsicgrowth rate is studied. We get the same relationship between it and the autonomousLotka-Volterra model, then we focus on the ω-limit sets of the two systems. Somenew results are obtained. For example, the solutions of the autonomous systemwhich originate in the same ray through the origin have the same ω-limit set.Specially, it implies that a local stable positive equilibrium will attract a cone with theapex at the origin.