Hyperchaos, qualitative analysis, control and synchronisation of a ten-term 4-D hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities

In this research work, a ten-term novel hyperchaotic system with an exponential nonlinearity and three quadratic nonlinearities has been derived. The Lyapunov exponents of the hyperchaotic system are obtained as L1 = 14.21985, L2 = 0.04417, L3 = 0 and L4 = −36.82311. Since the maximal Lyapunov exponent (MLE) of the novel hyperchaotic system is L1 = 14.21985, which is a large value, the novel hyperchaotic system exhibits strong chaotic behaviour. The Kaplan-Yorke dimension of the hyperchaotic system is obtained as DKY = 3.38736, which is a large value. Next, an adaptive control law has been designed to stabilise the novel hyperchaotic system with unknown system parameters. Moreover, an adaptive control law has been designed to achieve global hyperchaos synchronisation of the identical novel hyperchaotic systems with unknown system parameters. MATLAB simulations have been shown in detail to illustrate all the main results developed in this research work.

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