隐藏型混沌纠缠系统的存在特性

Existence characteristics of hidden chaotic entanglement system

为探究复杂混沌系统及其存在特性,构建了具有混沌纠缠函数的隐藏型混沌系统.首先,对新构建的三维系统进行动力学分析,发现系统包含周期吸引子共存和混沌吸引子共存等现象,表明该系统具有复杂的混沌特性和初值敏感性;其次,设计含有单一状态变量指数可变特点的动力学控制器,将三维系统转换为四维系统,分析四维系统在整数阶条件与分数阶条件下的动力学行为.经验证,当四维系统中单一状态变量指数取值改变时,整数阶与分数阶四维系统均是含有隐藏型吸引子的混沌纠缠系统,都存在指数取值趋于正无穷的可能性,且在分数阶条件下系统会出现超混沌现象.

To explore the complex chaotic system and its existence characteristics,a hidden chaotic system with chaotic entanglement function is constructed.Firstly,the dynamic analysis of the newly constructed three-dimensional system shows that the system includes the coexistence of periodic attractors and chaotic attractors.It indicates that the system has complex chaotic characteristics and initial value sensitivity.Secondly,a dynamic controller with single state variable is designed to convert the three-dimensional system into a four-dimensional system.The dynamic behavior of the four-dimensional system under the conditions of integer-order and fractional-order is analyzed.When the exponential value of a single state variable in a four-dimensional system changes,both integer order and fractional order four-dimensional systems are chaotic entangled systems with hidden attractors.There is a possibility that the exponential value approaches to positive infinity.Under fractional order condition,the system can appear hyperchaos.