Describing function based methods for predicting chaos in a class of fractional order differential equations
Describing function based methods for predicting chaos in a class of fractional order differential equations
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DOI：
10.1007/s11071-008-9447-y
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发表时间：
2009-08
影响因子：
5.6
通讯作者：
M. Tavazoei;M. Haeri
中科院分区：
文献类型：
--
作者：
M. Tavazoei;M. Haeri
本文讨论了两种预测分数阶微分方程混沌动力学的方法。这些方法，这是以前提出的经典整数阶系统中的混沌检测，是基于使用描述函数方法。其中一种方法是基于Genesio-Tesi猜想构造的混沌存在的方法，另一种方法是基于Hirai猜想介绍的非线性系统中发生混沌的方法。这些方法被重述用于预测2和3之间的阶数的分数阶微分方程的混沌。数值模拟结果表明，这些方法的能力，检测两个分数阶微分方程的二次和三次非线性的混沌。
This paper deals with two different methods for predicting chaotic dynamics in fractional order differential equations. These methods, which have been previously proposed for detecting chaos in classical integer order systems, are based on using the describing function method. One of these methods is constructed based on Genesio–Tesi conjecture for existence of chaos, and another method is introduced based on Hirai conjecture about occurrence of chaos in a nonlinear system. These methods are restated to use in predicting chaos in a fractional order differential equation of the order between 2 and 3. Numerical simulation results are presented to show the ability of these methods to detect chaos in two fractional order differential equations with quadratic and cubic nonlinearities.