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Describing function based methods for predicting chaos in a class of fractional order differential equations

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Abstract

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.

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Authors and Affiliations

  1. Advanced Control System Lab, Electrical Engineering Department, Sharif University of Technology, Tehran, Iran

    Mohammad Saleh Tavazoei & Mohammad Haeri

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  1. Mohammad Saleh Tavazoei
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  2. Mohammad Haeri
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Correspondence to Mohammad Haeri.

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Tavazoei, M.S., Haeri, M. Describing function based methods for predicting chaos in a class of fractional order differential equations. Nonlinear Dyn 57, 363–373 (2009). https://doi.org/10.1007/s11071-008-9447-y

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