Compounding self-excited and hidden attractors via a non-autonomous approach

Abstract

Compounding attractors, as an effective way to enhance the complexity of existing chaotic attractors, has attracted high attention. Various autonomous approaches have been devised to compound some self-excited attractors, but few involve non-autonomous approaches. Meanwhile, a universal and uncomplicated approach is still lacking. Focusing on non-autonomous domains, we propose a pulse control approach in this paper, which is directly applied to the constant terms of some known chaotic system equations to generate different types of compound self-excited and hidden attractors. Then, by setting the proper pulse signal functions we designed in this transformation, the number, shape, and size of these novel compound attractors are all controllable. The dynamical behaviors are theoretically analyzed, such as Lyapunov exponent spectra, bifurcation diagrams and so on. Furthermore, the corresponding hardware implementation by Field Programmable Gate Array (FPGA) is given. The hardware experimental results are consistent with the numerical simulations.