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Synchronization of fractional order Rabinovich-Fabrikant systems using sliding mode control techniques

Kumar Sanjay, Singh Chaman, Prasad Sada Nand, Shekhar Chandra, Aggarwal Rajiv

Archives of Control Sciences

2019

Vol. 29, No. 2

307--322

In this research article, we present the concepts of fractional-order dynamical systems and synchronization methodologies of fractional order chaotic dynamical systems using slide mode control techniques. We have analysed the different phase portraits and time-series graphs of fractional order Rabinovich-Fabrikant systems. We have obtained that the lowest dimension of Rabinovich-Fabrikant system is 2.85 through utilization of the fractional calculus and computational simulation. Bifurcation diagrams and Lyapunov exponents of fractional order Rabinovich-Fabrikant system to justify the chaos in the systems. Synchronization of two identical fractional-order chaotic Rabinovich-Fabrikant systems are achieved using sliding mode control methodology.