Local dynamics and bifurcation for a two-dimensional cubic Lotka-Volterra system (Part II)

The local bifurcation and dynamics for a two-dimensional cubic Kolmogorov system, depending on two small parameters, in certain hypotheses on the coefficients, are investigated. The paper continues the study performed in [4], by treating two non-generic cases, corresponding to the hypotheses that one of the significant coefficients vanishes. In the first non-generic case, the local dynamics is found to be similar to the one obtained in the generic case treated in [4]. In the second non-generic case new possibilities of behavior are found.