Chaos and Bifurcations of a Leslie-Gower Food Chain with Strong Allee Effect

Figure 4

Transcritical and saddle-node-Hopf bifurcations of system (7). (a) A transcritical bifurcation occurs when equilibria and collide at , where , , , , , , , and , where the black dash curve denotes stable equilibrium and the black solid curve denotes unstable equilibrium. (b) The double parameter bifurcation in the plane and other parameters take the same values as in (a), where the blue solid curve is Hopf bifurcation curve (HB) and the red solid line is saddle-node bifurcation curve. The intersection of HB curve and SNB curve is saddle-node-Hopf bifurcation (SN-Hopf).

(a)

(b)