基于多涡卷混沌系统的建模研究

Investigation and realization of a chaos system with multi-vortex

在Jerk系统的基础上,设计了多涡卷电路.通过用不同的分段函数构造非线性项,构造具有奇对称并且参量可调的非线性函数来扩展鞍焦平衡点.在x和y方向上拓展鞍焦平衡点,构造分布网格多涡卷混沌系统,做出1×6和6×6涡卷系统.调节合适的β系数,可以实现整个Jerk系统从周期态到混沌态.在此基础上,在分段函数的某区间内插入x^3,构造新的三维自治Jerk混沌系统,产生了不同涡卷的混沌现象.改造后的混沌吸引域更大,具有更好的加密掩盖性能.

A multi-vortex circuit was designed based on Jerk system.The saddle-focus equilibrium point was extended by constructing nonlinear terms with different piecewise functions with odd symmetry and adjustable parameters.In the xand ydirections,the saddle-focus equilibrium points were extended to construct the distributed grid multi-vortex chaotic system,and the 1×6 and 6×6 vortex systems were set up.By adjusting the appropriateβ,Jerk system could be realized from periodic state to chaotic state.On this basis,x^3 was inserted into an interval of piecewise function to construct a new three-dimensional autonomous Jerk chaotic system,which produced chaotic phenomena of different vortexes.The improved chaotic attractor domain was enlarged,and the encryption masking performance was enhanced.