Fractional-order chaotic system with hyperbolic function

Abstract

In this article, we study bistability, multiscroll, and symmetric properties of fractional-order chaotic system with cubic nonlinearity. The system is configured with hyperbolic function consisting of a parameter “g.” By varying the parameter “g,” the dynamical behavior of the system is investigated. Multistability and multiscroll are identified, which makes the system suitable for secure communication applications. When the system is treated as fractional order, for the same parameter values and initial conditions and when the fractional order is varied from 0.96 to 0.99, multiscroll property is obtained. Symmetric property is obtained for the order of 0.99. The fractional system holds only single scroll until 0.965 order and when the order increases to more than 0.99, it is having two-scroll attractor. This property opens a variety of applications for the systems, especially in secure communication. Adaptive synchronization of the system using sliding mode control scheme is presented. For implementing the fractional-order system in field-programmable gate array, Adomian decomposition method is used, and the register-transfer level schematic of the system is presented.