Dynamical behaviors of a two-competitive metapopulation system with impulsive control

Abstract

Abstract In this paper, we study the dynamical behaviors of a two-competitive metapopulation system with impulsive control and focus on the stable coexistence of the superior and inferior species. A Poincaré map is introduced to prove the existence of a periodic solution and its stability. It is also shown that a stably positive periodic solution bifurcates from the semi-trivial periodic solution through a transcritical bifurcation.

Keywords

• metapopulation system
• impulsive state feedback
• Poincaré map
• bifurcation