一个具有多稳定流的广义Hamiltonian保守混沌系统  

A generalized Hamiltonian conservative chaotic system with multi-stable flows

作　　者：贾红艳[1] 陈忠告 石文欣 韩晓光 JIA Hongyan;CHEN Zhonggao;SHI Wenxin;HAN Xiaoguang(College of Electronic Information and Automation,Tianjin University of Science and Technology,Tianjin 300222,China)

机构地区：[1]天津科技大学电子信息与自动化学院,天津300222

出　　处：《山东大学学报（工学版）》2022年第2期74-79,88,共7页Journal of Shandong University（Engineering Science）

基　　金：国家自然科学基金项目(61873186,61903274);天津市自然科学基金项目(17JCZDJC38300,18JCQNJC74000)。

摘　　要：通过分析一个三维保守混沌系统的力学和能量特性,发现当参数a=b时,该三维保守系统实际上是一个新的四维广义Hamiltonian保守系统的三维子系统。通过对新的广义Hamiltonian保守系统进行数值分析,如李雅普诺夫指数、分岔图、相轨迹等,发现其具有非常丰富的动力学行为:混沌特性、周期特性、拟周期特性。通过分析该广义Hamiltonian保守系统平衡点特性,发现其动力学行为呈现隐藏特性。同时,在系统参数不变的情况下,通过改变初值,发现该广义Hamiltonian保守系统具有多稳定性。利用现场可编程逻辑门阵列(field programmable gate array, FPGA)实现了该广义Hamiltonian保守系统,试验结果和数值分析结果是一致的。分别从数值分析和物理特性上验证了该广义Hamiltonian保守系统隐藏混沌特性和多稳定性的存在,为应用提供了新的模型。By analyzing the mechanical and energy properties of a three-dimensional conservative chaotic system, it was found that the three-dimensional conservative system was actually a three-dimensional subsystem of a new four-dimensional generalized Hamiltonian conservative system when the parameter a=b. By making numerical analysis for the new generalized Hamiltonian conservative system, such as Lyapunov exponents, bifurcation diagram, phase trajectory, etc., it was found that the new generalized Hamiltonian conservative system showed very rich dynamic behaviors: chaotic characteristics, periodic characteristics, quasi-periodic characteristics. By analyzing the equilibrium characteristics of the new generalized Hamiltonian conservative system, it was found that all dynamic behaviors were hidden. At the same time, when the system parameters remained unchanged, the new generalized Hamiltonian conservative system showed multi-stability by changing the initial values. The generalized Hamiltonian conservative system was implemented by utilizing field programmable gate array, and the results were in agreement with those from the numerical analysis. Hidden chaotic charactristics and multi-stability of the new generalized Hamiltonian conservative system were respectively verified by numerical analysis and physical properties, which provided a new model for application.

关 键 词：多稳定流 保守系统 混沌特性 隐藏特性 FPGA实现 

分 类 号：TP29[自动化与计算机技术—检测技术与自动化装置]