Chaotic Behavior Investigation and Synchronization of the Earth's Magnetic Field System

The problem of dynamical behavior and synchronization is investigated for the earth's magnetic field system in this paper. By construct a family of generalized radically infinite and positive definite Lyapunov functions, the globally attractive set and positively invariant set of the earth's magnetic field system are obtained. The chaotic behaviors of the earth's magnetic field system has been investigated by detailed numerical simulations results, such as phase portraits, bifurcation diagrams. A linear feedback controller is designed to achieve the global synchronization of two identical chaotic systems. Numerical simulations show the effectiveness of the method.