Complex dynamics in biological systems arising from multiple limit cycle bifurcation

In this paper, we study complex dynamical behaviour in biological systems due to multiple limit cycles bifurcation. We use simple epidemic and predator–prey models to show exact routes to new types of bistability, that is, bistability between equilibrium and periodic oscillation, and bistability between two oscillations, which may more realistically describe the real situations. Bifurcation theory and normal form theory are applied to investigate the multiple limit cycles bifurcating from Hopf critical point.