Characteristic analysis of a simple fractional-order chaotic system with infinitely many coexisting attractors and Its DSP implementation

Abstract

A new simple third-order chaotic system is proposed. The numerical solution of the proposed chaotic system is calculated by using the Adomian decomposition method. The phenomena of infinitely many coexisting attractors is found in this new chaotic system. This interesting physical phenomenon don’t disappear after fractional-order processing. Conversely, with the order of fractional-order system changes, it shows more complex dynamical characteristic than the original system. In particular, the dynamical behavior of the new fractional-order system is analyzed by using the methods of bifurcation diagram, complexity. Finally, the chaotic attractors are physically implemented by DSP experiment. An extremely simple chaotic system as the demonstration of the fractional-order characteristic, it is of great significance to the application of the special chaotic system in related fields.