Stability and bifurcation in a harvested one-predator–two-prey model with delays

It is known that one-predator–two-prey system with constant rate harvesting can exhibit very rich dynamics. If such a system contains time delayed component, it can have more interesting behavior. In this paper we study the effects of the time delay on the dynamics of the harvested one-predator–two-prey model. It is shown that time delay can cause a stable equilibrium to become unstable. By choosing the delay τ as a bifurcation parameter, we show that Hopf bifurcation can occur as the delay τ crosses some critical values. The direction and stability of the Hopf bifurcation are investigated by following the procedure of deriving normal form given by Faria and Magalhaes. An example is given and numerical simulations are finally performed for justifying the theoretical results.

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