School of Mathematics and Statistics

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Browsing School of Mathematics and Statistics by Subject "Active control"
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    Synchronization of different fractional order chaotic systems using active control
    ( 2010-11-01) Bhalekar, Sachin ; Daftardar-Gejji, Varsha
    Synchronization of fractional order chaotic dynamical systems is receiving increasing attention owing to its interesting applications in secure communications of analog and digital signals and cryptographic systems. In this article we utilize active control technique to synchronize different fractional order chaotic dynamical systems. Further we investigate the interrelationship between the (fractional) order and synchronization in different chaotic dynamical systems. It is observed that synchronization is faster as the order tends to one. © 2009 Elsevier B.V. All rights reserved.
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    Synchronization of fractional chaotic and hyperchaotic systems using an extended active control
    ( 2016-04-01) Bhalekar, Sachin
    An extended active control technique is used to synchronize fractional order chaotic and hyperchaotic systems with and without delay. The coupling strength is set to the value less than one to achieve the complete synchronization more easily. Explicit formula for the error matrix is also proposed in this chapter. Numerical examples are given for the fractional order chaotic Liu system, hyperchaotic new system and Ucar delay system. The effect of fractional order and coupling strength on the synchronization time is studied for non-delayed cases. It is observed that the synchronization time decreases with increase in fractional order as well as with increase in coupling strength for the Liu system. For the new system, the synchronization time decreases with increase in fractional order as well as with decrease in coupling strength.
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    Synchronization of non-identical fractional order hyperchaotic systems using active control
    ( 2014-02-01) Bhalekar, Sachin
    The problem of synchronization between non-identical hyperchaotic fractional order systems is discussed in this article. We use the method of active control to synchronize the chaotic trajectories. To illustrate the proposed theory, we consider two particular examples of synchronization in fractional order hyperchaotic systems viz. Rossler system with new system and Chen system with Lü system. The active control terms are chosen properly so as the errors in synchronization become zero after small duration of time. It is observed that the synchronization time decreases with increase in fractional order.