Analysis, Adaptive Control and Synchronization of a Novel 4-D Hyperchaotic Hyperjerk System via Backstepping Control Method

Abstract

Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system via backstepping control method SUNDARAPANDIAN VAIDYANATHAN A hyperjerk system is a dynamical system, which is modelled by an nth order ordinary differential equation with n 4 describing the time evolution of a single scalar variable. Equivalently, using a chain of integrators, a hyperjerk system can be modelled as a system of n first order ordinary differential equations with n 4. In this research work, a 4-D novel hyperchaotic hyperjerk system with two nonlinearities has been proposed, and its qualitative properties have been detailed. The novel hyperjerk system has a unique equilibrium at the origin, which is a saddle-focus and unstable. The Lyapunov exponents of the novel hyperjerk system are obtained as L 1 = 0.14219, L 2 = 0.04605, L 3 = 0 and L 4 = −1.39267. The Kaplan-Yorke dimension of the novel hyperjerk system is obtained as D KY = 3.1348. Next, an adaptive controller is designed via backstepping control method to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive controller is designed via backstepping control method to achieve global synchronization of the identical novel hyperjerk systems with three unknown parameters. MATLAB simulations are shown to illustrate all the main results derived in this research work on a novel hyperjerk system.

Variable universe adaptive fuzzy sliding mode projective synchronization of hyperjerk system based on disturbance observer

“…When n = 3 , system (1) degenerates into a jerk system. The main concerns of the researchers are the chaotic or hyperchaotic performance, control and synchronization of jerk system or hyperjerk system with such simple structures [2][3][4][5][6][7][8][9][10][11].…”

The Establishment and Dynamic Properties of a New 4D Hyperchaotic System with Its Application and Statistical Tests in Gray Images

“…At present, research on 1D chaos, such as Logistic mapping [ 5 , 6 , 7 ]; 2D chaos, such as Henon mapping [ 8 , 9 , 10 ]; and 3D chaos, such as Rossler chaotic attractor [ 11 , 12 , 13 ], Chua [ 14 , 15 , 16 ], and Chen [ 17 , 18 , 19 ], have been very extensive and mature. With the development of chaos theory, many people began to study high-dimensional chaotic attractors, such as 4D chaotic attractor subsystems [ 20 , 21 , 22 , 23 ], 5D chaotic attractor subsystems [ 24 , 25 , 26 , 27 ], and 6D chaotic attractor subsystems [ 28 ]. In recent years, fractional-order chaotic systems [ 29 , 30 , 31 ], hidden attractors [ 32 , 33 , 34 ], and chaotic systems with co-existing attractors [ 35 , 36 ] have also been extensively studied.…”

A New Nine-Dimensional Chaotic Lorenz System with Quaternion Variables: Complicated Dynamics, Electronic Circuit Design, Anti-Anticipating Synchronization, and Chaotic Masking Communication Application

“…Chaotic synchronization in physical, chemical, and biological systems has become an attractive subject in recent years and has a distinctly modern focus [3], with remarkable applications in secure communication. A secure communication system requires the development of a signal with the data that interceptors inside a carrier or transmitter signal must continue to remain undetectable.…”