Bifurcated periodic solutions in an amensalism system with strong generic delay kernel

The dynamics of an amensalism system with strong generic delay kernel is considered. From a careful analysis of characteristic equation, the local asymptotic stability of the positive equilibrium and the existence of Hopf bifurcation from the positive equilibrium are investigated, where the time delay is used as the bifurcation parameter. Moreover, we apply the normal form theory and the center manifold theorem to study the direction of these Hopf bifurcations and the stability of bifurcated periodic orbits. Finally, numerical simulations supporting the theoretical analysis are also included. Copyright © 2012 John Wiley & Sons, Ltd.