Chaotic and non-chaotic strange attractors of a class of non-autonomous systems

In this paper, the dynamics of a class of non-autonomous systems, generated from a unified chaotic autonomous system, is studied. It is found, via parameter modulation, that they have chaotic and non-chaotic strange attractors (NCSA). Several representative systems are constructed to illustrate the complex strange dynamics. The first example exhibits Lorenz-like behavior and Chen-like behavior at different time intervals. The second illustrates the existence of NCSA, which is constructed by “joining” the chaotic Chen system and a system with regular dynamics. The third is constructed based on the topological structure of the original autonomous systems, which has complex transient dynamics at the beginning, with a periodic orbit as the omega-limit set. The last one has quasi-periodic coefficients, yielding strange dynamics. These examples demonstrate that non-autonomous systems can have extremely rich and interesting dynamics under certain conditions.