Limit cycles in periodically perturbed population systems

Abstract

A perturbation method is proposed to calculate approximately the limit cycle type non-equilibrium steady-state resulting from periodic perturbation of coefficients of stable population systems; the two species Lotka-Volterra competition system is explicitly studied and the results are formulated for general multi-species population systems. Avoidance of competitive or other types of exclusion of species in a periodic environment is indicated.