Chaotic behaviors and toroidal/spherical attractors generated by discontinuous dynamics

This paper reports a class of chaotic attractors with toroidal or spherical patterns. These attractors look like spheres or tori, but they are not exactly on the two-dimensional toroidal/spherical surfaces. Discontinuous structures are taken in the considered system to produce easily various chaotic tori/spheres with different input functions. Moreover, controlling the shape of these chaotic attractors can be realized by adjusting some parameters with the help of Fourier series. The underlying chaos-generation mechanism is also explored briefly.