基于多涡卷混沌系统的建模研究
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摘要
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x3,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,x3 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.
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,x3 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.
引文
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[3]吕恩胜,张绘敏.一种n-涡卷Jerk系统及其电路设计[J].贵州师范大学学报(自然科学版),2014,32(6):51-56.
[4]王心华,江浩雨,冯娟娟,等.一类jerk混沌电路的仿真与设计[J].物理实验,2017,37(6):1-5.
[5]李亚,戴青云,卞丽雅,等.多涡卷Jerk混沌吸引子及其实现[J].中国图象图形学报,2008,13(3):443-447.
[6]俞清,姜盼,陆菱,等.基于Jerk形式的多涡卷混沌电路[J].常州大学学报(自然科学版),2016,28(2):83-87.
[7]孙克辉.混沌保密通信原理与技术[M].北京:清华大学出版社,2015:237-241
[2]禹思敏.混沌系统与混沌电路[M].西安:西安电子科技大学出版社,2011:240-243.
[3]吕恩胜,张绘敏.一种n-涡卷Jerk系统及其电路设计[J].贵州师范大学学报(自然科学版),2014,32(6):51-56.
[4]王心华,江浩雨,冯娟娟,等.一类jerk混沌电路的仿真与设计[J].物理实验,2017,37(6):1-5.
[5]李亚,戴青云,卞丽雅,等.多涡卷Jerk混沌吸引子及其实现[J].中国图象图形学报,2008,13(3):443-447.
[6]俞清,姜盼,陆菱,等.基于Jerk形式的多涡卷混沌电路[J].常州大学学报(自然科学版),2016,28(2):83-87.
[7]孙克辉.混沌保密通信原理与技术[M].北京:清华大学出版社,2015:237-241