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.