Analysis, adaptive control and synchronization of a novel 4-D hyperchaotic hyperjerk system and its SPICE implementation

Abstract

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 has been proposed, and its qualitative properties have been detailed. The Lyapunov exponents of the novel hyperjerk system are obtained asThe Kaplan-Yorke dimension of the novel hyperjerk system is obtained as D KY = 3.1573. Next, an adaptive backstepping controller is designed to stabilize the novel hyperjerk chaotic system with three unknown parameters. Moreover, an adaptive backstepping controller is designed to achieve global hyperchaos synchronization of the identical novel hyperjerk systems with three unknown parameters. Finally, an electronic circuit realization of the novel jerk chaotic system using SPICE is presented in detail to confirm the feasibility of the theoretical hyperjerk model.

Digital Image Encryption using Logistic Chaotic Key-based RC6

“…Owing to the ability of the logistic map to generate unpredictable and uncorrected characteristics, it has been used in the field of cryptography as a pseudorandom number generator, cryptographic algorithm and cryptanalysis [28][29][30][31].…”

A new 3-D jerk chaotic system with two cubic nonlinearities and its adaptive backstepping control

“…In the chaos literature, an impressive variety of techniques have been proposed for chaos synchronization such as active control method [109,110,111,112,113,114,115], adaptive control method [116,117,118,119,120,121,122,123,124,125,126,127], backstepping control method [128,129,130,131,132,133,134,135], sliding mode control method [136,137,138,139,140,141,142,143,144], etc.…”

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

“…Since the discovery of a first 4-D hyperchaotic system by Rössler in 1979 [52], many 4-D hyperchaotic systems have been found in the literature such as hyperchaotic Lorenz system [53], hyperchaotic Lü system [54], hyperchaotic Chen system [55], hyperchaotic Wang system [56], hyperchaotic Newton-Leipnik system [57], hyperchaotic Jia system [58], hyperchaotic Vaidyanathan systems [59,60,61,62,63,64,65,66,67,68], hyperchaotic Pham system [69], hyperchaotic Sampath system [70], etc.…”