Abstract:

 The stability and bifurcation of a single-species with interference and piecewise constant variables were discussed. Based on the theory of characteristic value, the necessary and sufficient conditions of the local asymptotically stability were obtained. The existence of Flip bifurcation and Hopf bifurcation were investigated by using center manifold argument and bifurcation theory. Some numerical simulations were performed by Matlab to verify the theoretical results.

Key words: interference; stability; Flip bifurcation; Hopf bifurcation