Abstract
This work announces a novel 4-D hyperjerk system with two cubic nonlinearities. The proposed chaotic system is an eight-term polynomial system with two cubic nonlinearities. The phase portraits of the novel hyperjerk system are displayed and the qualitative properties of the system are discussed. The novel hyperjerk system has a unique equilibrium, which is unstable. The Lyapunov exponents of the novel hyperjerk system are obtained as \(L_1 = 0.0622, L_2 = 0, L_3 = -0.4639\) and \(L_4 = -0.5945\), which shows that the novel hyperjerk system is chaotic. The Kaplan–Yorke dimension of the novel hyperjerk system is obtained as \(D_{KY} = 2.1341\). Next, an adaptive backstepping controller is designed to globally stabilize the novel hyperjerk system with unknown parameters. Moreover, an adaptive backstepping controller is also designed to achieve global chaos synchronization of the identical novel hyperjerk systems with unknown parameters. The main control results in this work are established using Lyapunov stability theory. MATLAB simulations have been shown to illustrate the phase portraits of the novel hyperjerk system and also the adaptive backstepping control results.
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Vaidyanathan, S. (2016). A Novel Hyperjerk System with Two Quadratic Nonlinearities and Its Adaptive Control. In: Vaidyanathan, S., Volos, C. (eds) Advances and Applications in Chaotic Systems . Studies in Computational Intelligence, vol 636. Springer, Cham. https://doi.org/10.1007/978-3-319-30279-9_3
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