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This paper studies the dynamical behaviors of a two-species competitive discrete model of plankton allelopathy. The system undergoes a flip bifurcation as we see by using the center manifold theorem and bifurcation theory. Numerical simulations not only illustrate our results, but they also exhibit the complex dynamical behaviors of the system, such as the period-doubling bifurcation in periods 2, 4, 8, and 16, and chaotic sets.

Bifurcation analysis of a two-species competitive discrete model of plankton allelopathy