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Co-existence of a Period Annulus and a Limit Cycle in a Class of Predator–Prey Models with Group Defense

    https://doi.org/10.1142/S0218127421501546Cited by:4 (Source: Crossref)

    For a family of two-dimensional predator–prey models of Gause type, we investigate the simultaneous occurrence of a center singularity and a limit cycle. The family is characterized by the fact that the functional response is nonanalytical and exhibits group defense. We prove the existence and uniqueness of the limit cycle using a new theorem for Liénard systems. The new theorem gives conditions for the uniqueness of a limit cycle which surrounds a period annulus. The results of this paper provide a mechanism for studying the global behavior of solutions to Gause systems through bifurcation of an integrable system which contains a center and a limit cycle.

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