A New Circumscribed Self-Excited Spherical Strange Attractor

Figure 4

Basin of attraction of system (1) with , , and in the ρ-θ plane with the fixed initial value of (a) and (b). All initial values of yellow color lead to the strange attractor of the system, and the purple ones lead to the unbounded orbits. The point which is shown in pink color leads to the equilibrium . The points represented in cyan color remain on the sphere of radius 10. Each unstable equilibria of the system can be seen in each represented basin of attraction. This helps to decide whether the attractor is self-excited or hidden.

(a)

(b)