两个耦合非自治振幅方程组的Smale-Williams型双曲吸引子
Hyperbolic attractor of Smale-Williams type in a system of two coupled non-autonomous amplitude equations
摘要：
最近，已经提出了具有Smal-Williams型的一致双曲吸引子的系统[Kuznetsov，Phys. Rev. Lett.，95，144101，2005]。该系统由两个耦合的非自治van der Pol振子组成，物理实现简单。本文引入了该系统的振幅方程，并证明了振幅方程组的吸引子也是一致双曲的。此外，我们表示定性说明以及定量特征的混沌动力学在这个吸引子。
英文摘要：
Recently, a system with uniformly hyperbolic attractor of Smale-Williams type has been suggested [Kuznetsov, Phys. Rev. Lett., 95, 144101, 2005]. This system consists of two coupled non-autonomous van der Pol oscillators and admits simple physical realization. In present paper we introduce amplitude equations for this system and prove that the attractor of the system of amplitude equations is also uniformly hyperbolic. Also we represent qualitative illustrations as well as quantitative characteristics of a chaotic dynamics on this attractor.
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