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Volume 2017, Article ID 1892618, 19 pages
Research Article

Fractional Order Memristor No Equilibrium Chaotic System with Its Adaptive Sliding Mode Synchronization and Genetically Optimized Fractional Order PID Synchronization

Centre for Non-Linear Dynamics, Defense University, Addis Ababa, Ethiopia

Correspondence should be addressed to Karthikeyan Rajagopal; moc.liamg@nayekeihtrakr

Received 12 October 2016; Revised 21 November 2016; Accepted 22 December 2016; Published 26 March 2017

Academic Editor: Ahmed G. Radwan

Copyright © 2017 Karthikeyan Rajagopal et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


This paper introduces a fractional order memristor no equilibrium (FOMNE) chaotic system and investigates its adaptive sliding mode synchronization. Firstly the dynamic properties of the integer order memristor no equilibrium system are analyzed. The fractional order memristor no equilibrium system is then derived from the integer order model. Lyapunov exponents and bifurcation with fractional order are investigated. An adaptive sliding mode control algorithm is derived to globally synchronize the identical fractional order memristor systems and genetically optimized fractional order PID controllers are designed and used to synchronize the FOMNE systems. Finally the fractional order memristor no equilibrium system is realized using FPGA.