Controlling Complex Dynamics in a Protected Area Discrete-Time Model

Figure 3

Phase plot with the parameters of Figure 1. (a) chaotic trajectory; (b) the stable fixed point before the Neimark-Sacker bifurcation occurs; (c) the Neimark-Sacker bifurcation; (d) the stable invariant closed curve around the fixed point created after bifurcation; (e) chaotic trajectory.

(a) 𝜎=0.165

(b) 𝜎=1.415

(c) 𝜎=1.4165

(d) 𝜎=1.42

(e) 𝜎=1.477