A fractional-order chaotic system with hidden attractor and self-excited attractor and its DSP implementation

Abstract

• A new 3 dimensional fractional order chaotic system with hidden attractor and self excited attractor is proposed. • The dynamical behaviors of FMACS self excited attractors and hidden attractors are explored separately with order q , and some comparisons are made by using LEs and bifurcation model. • The coexistence phenomenon of attractors in FMACS with hidden attractors is studied. It is interesting that attractors with different shapes appear in different orders. • FMACS is implemented on the DSP board. • A non linear term is replaced by e x , FMACS has a multi state transition and eventually quickly degenerates into a periodic state. The definition of fractional calculus is introduced into a 3D multi-attribute chaotic system in this paper. The fractional multi-attribute chaotic system (FMACS) numerical solution is obtained based on the Adomian decomposition method (ADM). The balance points and dynamical behaviors of self-excited and hidden attractors in FMACS are compared and analyzed through the Lyapunov spectrum, bifurcation model, and complexity. It is worth noting that some hidden coexistence attractors with different shapes are affected by the order. Besides, a novel chaotic system without equilibrium points is constructed, in which the nonlinear function term in FMACS is replaced with a rare nonlinear function e x . Meanwhile, its degradation phenomenon and state transition phenomenon are analyzed in detail. Finally, the digital circuit of the system is realized on the DSP board. The research result shows that FMACS has richer dynamical behaviors and higher complexity. This research provides a theoretical basis and guidance for the application of fractional chaotic systems.