Heteroclinic Cycles and Non-Transitive Competition in the Lotka-Volterra Model

The transient dynamics of the Lotka-Volterra competition model are closely related to the existence of heteroclinic cycles, which play a crucial role in understanding the phenomenon of non-transitive competition among species. In order to investigate the heteroclinic cycle topology of the Lotka-Volterra competition model, a MATLAB program was designed to determine the system parameters of the four-dimensional model. Under these parameters, it was found that the heteroclinic cycle of the system consists of four saddle points, with an outer limit cycle existing outside the heteroclinic cycle. The stability of the limit cycle was analyzed theoretically using the Routh-Hurwitz criterion and the Poincare normal form theory.