新光滑多翅膀混沌系统研究  

RESEARCH OF A NOVEL SMOOTH MULTI-WING CHAOTIC SYSTEM

作　　者：李文静 贾美美 Li Wenjing;Jia Meimei(College of Electric Power,Inner Mongolia University of Technology,Hohhot,010080 China;Key Laboratory of Electromechanical Control in Inner Mongolia Autonomous Region,Hohhot,010051 China)

机构地区：[1]内蒙古工业大学电力学院,呼和浩特010080 [2]内蒙古自治区机电控制重点实验室,呼和浩特010051

出　　处：《动力学与控制学报》2021年第4期16-24,共9页Journal of Dynamics and Control

基　　金：内蒙古自治区自然科学基金资助项目(2017BS0603)。

摘　　要：针对光滑多翅膀混沌系统不易于构造的问题,基于光滑代数函数提出两个新光滑多分段非线性函数,并用新光滑多分段非线性函数构造了新光滑单方向多翅膀S-M混沌系统和新光滑二方向网格多翅膀S-M混沌系统.然后,分析了两个新光滑多翅膀混沌系统的非线性动力学行为,主要包括相图、平衡点、不变性、耗散性、李亚普诺夫指数、分维数和庞加莱截面,并得到了多翅膀混沌吸引子的产生机理.其产生机理为指标2鞍焦平衡点用于产生翅膀.此外,通过单方向多翅膀S-M混沌吸引子和二方向网格多翅膀S-M混沌吸引子的电路实现,验证了理论推导和数值仿真的正确性.It is difficult to construct smooth multi-wing chaotic systems.This paper proposes two novel smooth multisegment nonlinear functions based on a smooth algebraic function,and constructs two new chaotic systems,e.g.,a one-direction multi-wing S-M one and a two-direction grid multi-wing S-M one,by using the proposed multisegment nonlinear functions.Then,the nonlinear dynamic behaviors of two smooth multi-wing chaotic systems are analyzed,with phase diagrams,equilibrium points,invariance,dissipation,Lyapunov exponents,fractal dimension,Poincarésection,and the generation mechanism of the multi-wing chaotic attractors being obtained.The generation mechanism is that the saddle-focus equilibrium points with index 2 are responsible for generating wings.In addition,the circuit implementations of the one-direction multi-wing S-M chaotic attractors and the two-direction grid multi-wing S-M chaotic attractors validate theoretical results and numerical simulations.

关 键 词：非线性动力学行为 多翅膀混沌系统 代数函数 多分段非线性函数 电路实现 

分 类 号：O415.5[理学—理论物理]