Design and SPICE implementation of a 12-term novel hyperchaotic system and its synchronisation via active control

This research work describes the design and SPICE implementation of a 12-term novel hyperchaotic system with four quadratic nonlinearities. The Lyapunov exponents of the dissipative novel hyperchaotic system are obtained as L1 = 4.1043, L2 = 0.1571, L3 = 0 and L4 = −34.2529. The maximal Lyapunov exponent (MLE) of the novel hyperchaotic system is L1 = 4.1043. The Lyapunov dimension of the hyperchaotic system has been obtained as DL = 3.1244. The qualitative properties of the novel hyperchaotic system are described in detail. Moreover, the hyperchaotic system has been implemented in LTspice IV (SPICE simulator) and the outputs are obtained in SPICE showing hyperchaos of the novel system. Next, active control method has been applied for the global synchronisation of the novel hyperchaotic systems and the synchronisation result has been proved using Lyapunov stability theory. The active controller for the global synchronisation of the identical novel hyperchaotic systems has been implemented in LTspice IV and the SPICE simulation results have been detailed.