Chaos in the fractional order unified system and its synchronization
Chaos in the fractional order unified system and its synchronization
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DOI：
10.1016/j.jfranklin.2007.11.003
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发表时间：
2008-07
期刊：
影响因子：
--
通讯作者：
Xiang-Jun Wu;Jie Li;Guanrong Chen
中科院分区：
文献类型：
--
作者：
Xiang-Jun Wu;Jie Li;Guanrong Chen
对分数阶统一系统的混沌行为进行了数值研究。利用分数阶微积分技术，我们发现在阶数小于3的分数阶统一系统中存在混沌。我们在这个系统中发现的最低混沌阶数是2.76。采用单向耦合方法对分数阶统一系统的混沌同步进行了理论和数值研究。利用拉普拉斯变换理论，导出了分数阶微分系统实现同步的适宜条件。注意到驱动系统和响应系统实现同步所需的时间和同步效果敏感地依赖于耦合强度。通过数值模拟验证了理论分析的正确性。
The chaotic behaviors in the fractional order unified system are numerically investigated. By utilizing the fractional calculus techniques, we found that chaos exists in the fractional order unified system with order less than 3. The lowest order we found to have chaos in this system is 2.76. Chaos synchronization of the fractional order unified system is theoretically and numerically studied using the one-way coupling method. The suitable conditions for achieving synchronization of the fractional order differential system are derived by using the Laplace transform theory. It is noticed that the time required for achieving synchronization of the drive system and the response system and the synchronization effect sensitively depend on the coupling strength. Numerical simulations are performed to verify the theoretical analysis.