Analysis and Application Using Quad Compound Combination Anti-synchronization on Novel Fractional-Order Chaotic System
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RESEARCH ARTICLE-SYSTEMS ENGINEERING
Analysis and Application Using Quad Compound Combination Anti-synchronization on Novel Fractional-Order Chaotic System Lone Seth Jahanzaib1 · Pushali Trikha1 · Dumitru Baleanu2,3,4 Received: 10 June 2020 / Accepted: 1 September 2020 © King Fahd University of Petroleum & Minerals 2020
Abstract In this manuscript, a novel fractional-order chaotic model has been investigated. The characteristic dynamics of the model have been investigated using various tools such as Lyapunov dynamics, bifurcation diagrams, equilibrium point analysis, Kaplan York dimension, existence and uniqueness of solution. The Lyapunov spectrum, bifurcation diagrams and attractors are discussed over a range of fractional order of 0.8 to 1. The considered system is synchronized by using a novel technique quad compound combination anti-synchronization using two control methods, viz. nonlinear and adaptive sliding mode technique. The obtained results of synchronization are compared with some existing literature and also illustrated its application in secure communication. Keywords Dynamical analysis · Quad compound combination anti-synchronization · Adaptive sliding mode control · Nonlinear control · Secure communication
1 Introduction Fractional-order systems are one of the significant classes of nonlinear systems. They have been used widely in many real-world applications such as image processing [1], fractional control, secure communication [2], cryptography [3], geo-sciences [4] and so on. The fractional calculus have an advantage over integer calculus because of its significance in describing natural systems and representing hereditary properties of systems with more accuracy. Because of these properties, the future of mathematical modeling has been clubbed with the fractional calculus. With the advancement of net-
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Dumitru Baleanu [email protected] Lone Seth Jahanzaib [email protected] Pushali Trikha [email protected]
1
Department of Mathematics, Jamia Millia Islamia, New Delhi 110025, India
2
Department of Mathematics, Cankaya University, Ögretmenler Cad, 1406530 Ankara, Turkey
3
Institute of Space Sciences, Magurele, Bucharest, Romania
4
Department of Medical Research, China Medical University Hospital, China Medical University, Taichung, Taiwan
work, communication and computer technologies, security issues of information have attracted more attention and become a research hot spot. Chaos has characteristics such as pseudo-randomness, unpredictability and extreme sensitivity to initial values. These properties have been exploited for applications in memristors, complex numbers, random number generators, etc. Recently designing of fractional chaotic and hyper chaotic systems [5–8] having specific properties is gaining popularity. Analyzing chaotic systems [9–12] for their attractor structures, self-excited and hidden attractors, number of equilibrium points [13], stable and unstable equilibrium points, hyperbolic and nonhyperbolic equilibrium points highlights the rich dyn
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