新光滑多翅膀混沌系统研究

RESEARCH OF A NOVEL SMOOTH MULTI-WING CHAOTIC SYSTEM

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.