科研之友
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摘要
describes the simplest electronic circuit which can have chaotic phenomena. In this paper, we first prove the existence of three families of consecutive periodic orbits of the system when alpha = 0, two of which are located on consecutive invariant surfaces and form two invariant topological cylinders. Then we prove that for alpha > 0 if the system has a periodic orbit or a chaotic attractor, it must intersect both of the planes z = 0 and z = - 1 infinitely many times as t tends to infinity. As a byproduct, we get an example of unstable invariant topological cylinders which are not normally hyperbolic and which are also destroyed under small perturbations.
- 出版日期2013-8
- 单位上海交通大学
