The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to th...The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.展开更多
目前针对分数阶混沌系统的研究大多数都是基于DSP(Digital Signal Processor)平台,由于分数阶混沌系统的复杂度较大,用DSP实现存在序列生成速度较慢的问题,只能应用于对速度要求不高的系统.针对该问题,研究了基于分数阶微积分Grunwald-L...目前针对分数阶混沌系统的研究大多数都是基于DSP(Digital Signal Processor)平台,由于分数阶混沌系统的复杂度较大,用DSP实现存在序列生成速度较慢的问题,只能应用于对速度要求不高的系统.针对该问题,研究了基于分数阶微积分Grunwald-Letnikov(GL)定义的分数阶简化Lorenz系统的FPGA(field programmable gate array)实现.通过最大Lyapunov指数和0~1测试验证了基于GL定义的分数阶简化Lorenz系统是混沌的.详细分析了基于GL定义的分数阶简化Lorenz系统的FPGA实现结构,并使用定点数格式实现了该系统.通过示波器观察FPGA输出结果与MATLAB仿真结果一致,从而进一步揭示了分数阶混沌系统的可实现性.展开更多
基金supported by the Natural Science Foundation of Hebei Province,China (Grant Nos A2008000136 and A2006000128)
文摘The chaotic behaviours of a fractional-order generalized Lorenz system and its synchronization are studied in this paper. A new electronic circuit unit to realize fractional-order operator is proposed. According to the circuit unit, an electronic circuit is designed to realize a 3.8-order generalized Lorenz chaotic system. Furthermore, synchronization between two fractional-order systems is achieved by utilizing a single-variable feedback method. Circuit experiment simulation results verify the effectiveness of the proposed scheme.
