用鞍焦同位轨道生成混沌

Int. J. Bifurc. Chaos Pub Date : 2024-01-01 DOI:10.1142/s0218127424500111

Chaoxia Zhang, Shangzhou Zhang, Yuqing Zhang

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摘要

本文基于两个混沌化判据，即所有轨道均为全局有界且Lyapunov指数为正，提出了一种反控制方法，以设计具有鞍焦同轴轨道的三维连续时间自主混沌系统。利用Shil'nikov定理，在设计的受控系统中发现了原点附近的Poincaré回归图，证实了Smale马蹄铁意义上混沌的存在。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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Generating Chaos with Saddle-Focus Homoclinic Orbit

This paper develops an anticontrol approach to design a 3D continuous-time autonomous chaotic system with saddle-focus homoclinic orbit, based on two chaotification criterions for all orbits to be globally bounded with positive Lyapunov exponents. By using the Shil’nikov theorem, a Poincaré return map near the origin is found in the designed controlled system, confirming the existence of chaos in sense of the Smale horseshoe.

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Int. J. Bifurc. Chaos

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