拟Lorenz方程在周期扰动下的奇怪吸引子

摘要

It was studied the dynamics of strange attractors in a periodically perturbed Lorenz-like equation through numerical simulation. Three types of strange attractors associated with homoclinic tangles; sink, H(e)non-like attractors and rank-one attractors were observed. Sinks represented the perturbed equation had attractive period solution. Henon-like attractors and rank-one attractors represented chaotic behaviors characterized by SRB measures. It was illustrated that these three types of strange attractors occur repeatedly in a fixed pattern as the magnitude of the perturbation approached to zero. The study followed the line of the recent studies on periodically perturbed two-dimensional system and the obtained results generalized these previous studies to three-dimensional equations.%通过数值模拟研究一类拟Lorenz周期扰动方程,得到3类同宿缠结吸引子:周期汇、似Hénon吸引子和秩一吸引子.其中周期汇表示扰动方程出现吸引的周期轨,而似Hénon吸引子和秩一吸引子表示扰动方程出现SRB测度意义下的混沌现象.进一步,当扰动参数趋于零时,这3类吸引子重复出现,呈现一定的周期性.所得结果是二维同宿缠结理论在三维空间中的应用和推广.