Stability and bifurcation of a two competing prey-one predator system with anti-predator behavior

Debasis Mukherjee


This article considers the impact of competitive response to interfering time and anti-predator behavior of a three species system in which one predator consumes both the competing prey species. Here one of the competing species shows anti-predator behavior. We have shown that its solutions are non-negative and bounded. Further, we analyze the existence and stability of all the feasible equilibria. Conditions for uniform persistence of the system are derived. Applying Bendixson’s criterion for high-dimensional ordinary differential equations, we prove that the coexistence equilibrium point is globally stable under specific conditions. The system admits Hopf bifurcation when anti-predator behavior rate crosses a critical value. Analytical results are verified numerically.


Competitive response; anti-predator behavior; interfering time; persistence; stability analysis; Hopf bifurcation

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