具有共存混沌吸引子的超大范围参数混沌系统

A super-wide-range parameter chaotic system with coexisting chaotic attractor

为了使参数在超大范围内变化时系统均具有共存吸引子,构建新型的双翼与四翼吸引子共存的混沌系统.系统的状态方程共有7项,在每个状态方程中只有1个非线性项,且此非线性项是由另外2个状态变量的乘积组成的.分析系统的稳定性、系统特性对参数变化的敏感性、系统参数在超大范围内变化时吸引子的共存特性等.研究结果表明,在参数α作微小变化时,系统特性具有较强的敏感性;当仅改变初始值的大小时,系统具有2个孤立双翼混沌吸引子与1个四翼混沌吸引子共存的特性;当参数d∈(0,2×10^4]时,系统同样具有混沌吸引子,且均具有共存的2个孤立双翼混沌吸引子与1个四翼混沌吸引子.此外,设计系统的硬件电路,利用Multisim进行电路仿真,进一步验证参数在超大范围内变化时系统中共存吸引子的存在性.

Aiming at obtaining a chaotic system with a super wide parameter range and coexisting attractors,a novel chaotic system with coexisting two-wing and four-wing attractors was constructed.There are seven items in each system state equation,of which there is only one nonlinear item.This nonlinear item is composed of the product of other two state variables.The stability of the system,the sensitivity of the system characteristics to parameter variation and the coexisting characteristics of attractors against the super-wide-range system parameter were analyzed.Results showed that the system characteristics had a strong sensitivity when parameter a was slightly changed,and the system had the characteristics of coexistence of two isolated two-wing chaotic attractors and one four-wing chaotic attractor when only the initial value was changed,and the system had coexisting chaotic attractors namely two isolated two-wing chaotic attractors and one four-wing chaotic attractor for parameter d∈(0,2×10^4].In addition,a hardware circuit of the system was designed and circuit simulation was conducted by Multisim.The existence of coexisting attractors under the wide variation range of parameters was further verified.