Hyperchaos, adaptive control, synchronization, and electronic circuit design of a novel 6D hyperchaotic convective dynamo system

In this work, a new nonlinear dynamic (6D) system of equations is proposed that describes the process of magnetic field generation. This system of equations is an alternative to the Rikitake dynamo system describing chaotic magnetic field reversals.

The behavior of the new dynamical system is studied by analyzing the stability of equilibrium points. For fixed parameters of the 6D dynamical system, the spectrum of Lyapunov exponents and the Kaplan-York dimension are calculated. The presence of two positive Lyapunov exponents demonstrates the hyperchaotic behavior of the 6D dynamical system. The fractional Kaplan-York dimension indicates the fractal structure of strange attractors. We have shown that an adaptive controller is used to stabilize the novel 6D chaotic system with unknown system parameters. An active control method is derived to achieve global chaotic synchronization of two identical novels 6D chaotic systems with unknown system parameters.

Based on the results obtained in Matlab-Simulink and LabVIEW models, a chaotic signal generator for the 6D chaotic system is implemented in the Multisim environment. The results of chaotic behavior simulation in the Multisim environment show similar behavior when comparing simulation results in Matlab-Simulink and LabVIEW models.