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Chaos Synchronization of a New Chaotic System Having Exponential Term Via Adaptive and Sliding Mode Control

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Abstract

In this paper, we have introduced a new three-dimensional system having exponential term. The chaotic nature of the system is analysed by examining the Lyapunov exponents, graphing the phase portraits, time series of state vectors, bifurcation diagram, and Poincare maps. The novel system has three equilibrium points and it is discussed that all equilibrium points are unstable in nature. The two schemes of adaptive control and sliding mode control for chaos synchronization have been discussed for the novel chaotic system. Suitable nonlinear controllers have been designed in both adaptive control and sliding mode control methods to achieve the desired synchronization between identical chaotic systems by using the Lyapunov stability theory and Vaidyanathan’s theorem. Numerical simulations have been performed and the graphs are presented using MATLAB.

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  1. Dinesh Khattar and Neha Agrawal have contributed equally to this work.

Authors and Affiliations

  1. Department of Mathematics, Kirori Mal College, University of Delhi, New Delhi, Delhi, 110007, India

    Dinesh Khattar, Neha Agrawal & Govind Singh

  2. Department of Mathematics, Indian Institute of Technology, Delhi, IITD, New Delhi, Delhi, 110016, India

    Govind Singh

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  1. Dinesh Khattar
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Khattar, D., Agrawal, N. & Singh, G. Chaos Synchronization of a New Chaotic System Having Exponential Term Via Adaptive and Sliding Mode Control. Differ Equ Dyn Syst (2023). https://doi.org/10.1007/s12591-023-00635-0

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