A No-Equilibrium Hyperchaotic System and Its Fractional-Order Form

Abstract EN

No-equilibrium system with chaotic behavior has attracted considerable attention recently because of its hidden attractor.

We study a new four-dimensional system without equilibrium in this work.

The new no-equilibrium system exhibits hyperchaos and coexisting attractors.

Amplitude control feature of the system is also discovered.

The commensurate fractional-order version of the proposed system is studied using numerical simulations.

By tuning the commensurate fractional-order, the proposed system displays a wide variety of dynamical behaviors ranging from coexistence of quasiperiodic and chaotic attractors and bistable chaotic attractors to point attractor via transient chaos.