Chaos, feedback control and synchronization of a fractional-order modified Autonomous Van der Pol-Duffing circuit
Chaos, feedback control and synchronization of a fractional-order modified Autonomous Van der Pol-Duffing circuit
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DOI：
10.1016/j.cnsns.2010.04.027
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发表时间：
2011-02-01
影响因子：
3.9
通讯作者：
Matouk, A. E.
中科院分区：
文献类型：
--
作者：
Matouk, A. E.
本文利用分数 Routh-Hurwitz 准则，研究了分数阶改良自主范德波尔-杜芬（MAVPD）电路的稳定性分析。得出了该系统保持混沌的必要条件。研究发现，该系统中存在阶数小于 3 的混沌。此外，还利用分数 Routh-Hurwitz 条件将所提出的分数阶系统中的混沌控制到其均衡状态。根据分数 Routh-Hurwitz 条件，并使用特定的线性控制器，结果表明分数阶 MAVPD 系统被控制到了其平衡点；但其整数阶对应系统却没有被控制。此外，在使用特定的非线性控制函数时，只有在分数阶情况下才能发现 MAVPD 系统的混沌同步。这说明了分数阶对混沌控制和同步的影响。使用单向线性误差反馈耦合方法也能实现同步。数值结果表明了理论分析的有效性。(C) 2010 Elsevier B.V. 版权所有。保留所有权利。
In this work, stability analysis of the fractional-order modified Autonomous Van der Pol-Duffing (MAVPD) circuit is studied using the fractional Routh-Hurwitz criteria. A necessary condition for this system to remain chaotic is obtained. It is found that chaos exists in this system with order less than 3. Furthermore, the fractional Routh-Hurwitz conditions are used to control chaos in the proposed fractional-order system to its equilibria. Based on the fractional Routh-Hurwitz conditions and using specific choice of linear controllers, it is shown that the fractional-order MAVPD system is controlled to its equilibrium points; however, its integer-order counterpart is not controlled. Moreover, chaos synchronization of MAVPD system is found only in the fractional-order case when using a specific choice of nonlinear control functions. This shows the effect of fractional order on chaos control and synchronization. Synchronization is also achieved using the unidirectional linear error feedback coupling approach. Numerical results show the effectiveness of the theoretical analysis. (C) 2010 Elsevier B.V. All rights reserved.