Self-Excited and Hidden Chaotic Attractors in Matouk’s Hyperchaotic Systems

Figure 9

3D view of multihidden attractors in the fractional-order Matouk’s system, with the fractional parameter and initial conditions for green trajectory, for red trajectory, and for blue trajectory, showing the following: (a) coexisting unstable saddle-focus attractors for (b) coexisting homoclinic orbits for (c) coexisting invariant closed curves for (d) coexisting higher periodic orbits and homoclinic orbits for and (e) existence of strange hidden chaotic attractor in the integer-order Matouk’s system, with using initial conditions for green trajectory.

(a)

(b)

(c)

(d)

(e)