A new nonlinear oscillator with infinite number of coexisting hidden and self-excited attractors

In this paper, we introduce a new two-dimensional nonlinear oscillator with an infinite number of coexisting limit cycles. These limit cycles form a layer-by-layer structure which is very unusual. Forty percent of these limit cycles are self-excited attractors while sixty percent of them are hidden attractors. Changing this new system to its forced version, we introduce a new chaotic system with an infinite number of coexisting strange attractors. We implement this system through field programmable gate arrays.