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中文摘要：
基于三阶单涡卷混沌Colpitts振荡器模型,通过引入两个分段线性三角波函数,构造了一个新型四维多涡卷超混沌系统,生成了（2M＋1）×（2N＋1）,（2M＋1）和（2N＋1）涡卷混沌和超混沌吸引子.利用相轨图、Poincar啨映射、Lyapunov指数谱和分岔图等方法,对新提出的四维多涡卷超混沌系统进行了动力学分析,结果表明,多涡卷超混沌系统的Hopf分岔点仅与控制参数有关,而涡卷数量和控制参数的混沌和超混沌范围随着转折点数量的增加而增加.此外,设计了一个实现四维多涡卷超混沌系统的模拟电路,实验输出与数值仿真的两个结果基本一致.
英文摘要：
Based on third-order spiral chaotic Colpitts oscillator model, by introducing two piecewise-linear triangular function, a novel four-dimensional multi-scroll hyperchaotic system is constructed, which can generate （2M＋1） ×（2N＋1）, （2M＋1） and （2N＋1）-scroll chaotic and hyperchaotic attractors. By using phase portrait, Poincaré mapping, Lyapunov exponent spectrum and bifurcation diagram, the dynamical behaviors of the proposed multi-scroll hyperchaotic system are analyzed. These results indicate that Hopf bifurcation point of multi-scroll hyperchaotic system is only related with the control parameter, but its scroll number and ranges of the control parameter for chaotic and hyperchaotic states increase along with the number of turning points. Furthermore, an analog circuit was designed to realize the four-dimensional multi-scroll hyperchaotic system. The results of experimental output and numerical simulation are basically the same.
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