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Stability analysis of fractional-order generalized chaotic susceptible–infected–recovered epidemic model and its synchronization using active control method

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Abstract

This paper presents the synchronization between a pair of identical susceptible–infected–recovered (SIR) epidemic chaotic systems and fractional-order time derivative using active control method. The fractional derivative is described in Caputo sense. Numerical simulation results show that the method is effective and reliable for synchronizing the fractional-order chaotic systems while it allows the system to remain in chaotic state. The striking features of this paper are: the successful presentation of the stability of the equilibrium state and the revelation that time for synchronization varies with the variation in fractional-order derivatives close to the standard one for different specified values of the parameters of the system.

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Acknowledgements

This work is supported by TCS Research Scholar Programme, Tata Consultancy Services Limited, India. The authors are grateful to the revered reviewers for their pertinent suggestions which have immensely helped them to improve the presentation of this paper.

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  1. Department of Mathematical Sciences, Indian Institute of Technology (BHU), Varanasi, 221 005, India

    SANA P ANSARI, SAURABH K AGRAWAL & SUBIR DAS

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  1. SANA P ANSARI
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  2. SAURABH K AGRAWAL
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  3. SUBIR DAS
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Correspondence to SUBIR DAS.

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ANSARI, S.P., AGRAWAL, S.K. & DAS, S. Stability analysis of fractional-order generalized chaotic susceptible–infected–recovered epidemic model and its synchronization using active control method. Pramana - J Phys 84, 23–32 (2015). https://doi.org/10.1007/s12043-014-0830-6

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  • DOI: https://doi.org/10.1007/s12043-014-0830-6

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