Advances and Applications in Chaotic Systems pp 163-187 | Cite as

# Adaptive Control and Circuit Simulation of a Novel 4-D Hyperchaotic System with Two Quadratic Nonlinearities

## Abstract

This work describes a ten-term novel 4-D hyperchaotic system with two quadratic nonlinearities. The phase portraits of the novel hyperchaotic system are depicted and the qualitative properties of the novel hyperchaotic system are discussed. The novel hyperchaotic system has a unique equilibrium at the origin, which is a saddle point. The Lyapunov exponents of the novel hyperchaotic system are obtained as \(L_1 = 1.0784, L_2 = 0.1114, L_3 = 0\) and \(L_4 = -18.1714\), while the Kaplan–Yorke dimension of the novel hyperchaotic system is obtained as \(D_{KY} = 3.0655\). Since the sum of the Lyapunov exponents is negative, the novel hyperchaotic system is dissipative. Next, an adaptive controller is designed to globally stabilize the novel hyperchaotic system with unknown parameters. Moreover, an adaptive controller is also designed to achieve global chaos synchronization of the identical hyperchaotic systems with unknown parameters. MATLAB simulations are depicted to illustrate all the main results derived in this work. Finally, an electronic circuit realization of the novel hyperchaotic system using Spice is presented in detail to confirm the feasibility of the theoretical model.

## Keywords

Chaos Chaotic systems Hyperchaos Hyperchaotic systems Adaptive control Synchronization Circuit simulation## References

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