Heteroclinic Cycles and Transient Dynamics in the Four-Dimensional Lotka-Volterra Competition Model

The transient dynamics of the Lotka-Volterra competition model are closely associated with the presence of heteroclinic cycles, which play a vital role in understanding the phenomenon of non-transitive competition among species. To investigate the heteroclinic cycle topology of the Lotka-Volterra competition model, a MATLAB program is designed to determine the system parameters of the four-dimensional model. Under these parameters, it is discovered that the system's heteroclinic cycle is composed of four saddle points, with an outer limit cycle existing outside the heteroclinic cycle. The stability of the limit cycle is theoretically analyzed using the Routh-Hurwitz criterion and the Poincare normal form theory.