Abstract

This paper develops a design method for the interconnections of a network of Andronov–Hopf oscillators such that the system exhibits a desired strange attractor. Because of the structure of the oscillators, the desired behavior can be achieved via weak linear coupling, which destabilizes the oscillators’ phase difference. First, a set of sufficient conditions are established that result in phase destabilization, and thus instability, of a desired periodic solution. Then, an additional condition is determined to ensure that all harmonic periodic orbits will be unstable. Finally, additional numerical properties are assessed, where tuning of a small parameter can result in chaos.

中文翻译：

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具有所需奇异吸引子的Andronov-Hopf耦合振荡器的设计

摘要

本文开发了一种用于Andronov-Hopf振荡器网络互连的设计方法，以使系统表现出所需的奇异吸引子。由于振荡器的结构，可以通过弱线性耦合来实现所需的行为，这会破坏振荡器的相位差。首先，建立了一组充分的条件，这些条件导致所需的周期解的相不稳定，从而导致不稳定。然后，确定附加条件以确保所有谐波周期轨道将不稳定。最后，还要评估其他数值属性，其中小的参数调整会导致混乱。