Hidden attractors in a new fractional-order Chua system with arctan nonlinearity and its DSP implementation

Abstract

This paper reports a new fractional-order Chua’s system with arctan function and an algorithm for determining the initial value of fractional-order hidden attractors. Firstly, dynamics of the system is investigated by employing the stability analysis, dissipativeness, phase diagrams, 0-1 test, bifurcation diagram and SampEn complexity measure. It shows rich dynamics in the proposed system. Secondly, using the proposed algorithm, the initial values of the new fractional-order Chua’s system are calculated. And according to two sets of initial conditions, hidden attractors are found and verified by the numerical simulation. Meanwhile, the basin attraction is analyzed to confirm that the hidden attractor is indeed not near the fixed point. Thirdly, the new fractional-order Chua’s system is implemented on the DSP platform, and the arctan function’s processing algorithm is proposed. The DSP experimental results show that the system can produce a pair of coexisting fractional-order hidden attractors, and the experimental results are consistent with the numerical simulation results. It verifies the effectiveness of the presented methods and shows the potential engineering application value of the proposed Chua’s system.

Keywords

• Chaotic system
• Chua’s system
• Digital circuit
• Hidden attractors