Chaos and Symbol Complexity in a Conformable Fractional-Order Memcapacitor System

• Published in: Complexity (New York, N.Y.) Vol. 2018; no. 2018; pp. 1 - 15
• Main Authors: He, Shaobo, Yan, Bo, Banerjee, Santo
• Format: Journal Article
• Language: English
• Published: Cairo, Egypt Hindawi Publishing Corporation 01-01-2018; Hindawi; John Wiley & Sons, Inc; Hindawi Limited; Hindawi-Wiley
• Subjects: Algorithms; Analysis; Bifurcations; Chaos theory; Circuits; Complexity; Dynamical systems; Entropy; Fault diagnosis; Fractional calculus; Laplace transforms; Mathematical models; Nonlinear dynamics; Nonlinear systems; Numerical analysis; Ordinary differential equations; Pseudorandom sequences; Researchers; Time series
• ISSN: 1076-2787; 1099-0526
• DOI: 10.1155/2018/4140762

Application of conformable fractional calculus in nonlinear dynamics is a new topic, and it has received increasing interests in recent years. In this paper, numerical solution of a conformable fractional nonlinear system is obtained based on the conformable differential transform method. Dynamics of a conformable fractional memcapacitor (CFM) system is analyzed by means of bifurcation diagram and Lyapunov characteristic exponents (LCEs). Rich dynamics is found, and coexisting attractors and transient state are observed. Symbol complexity of the CFM system is estimated by employing the symbolic entropy (SybEn) algorithm, symbolic spectral entropy (SybSEn) algorithm, and symbolic C0 (SybC0) algorithm. It shows that pseudorandom sequences generated by the system have high complexity and pass the rigorous NIST test. Results demonstrate that the conformable memcapacitor nonlinear system can also be a good model for real applications.