Synchronization dependence on initial setting of chaotic systems without equilibria

An initial-dependent system is developed from an electromotor driven by nonlinear torque. Standard nonlinear analysis is carried out and chaotic region is explored in the dynamical system without equilibria. Phase portrait, Lyapunov exponent spectrum, Hamilton energy and bifurcation analysis are calculated to confirm the emergence of chaos and state selection. It is found that the attractor type (periodical or chaotic) is dependent on the initial setting. Furthermore, bidirectional coupling is used to detect the synchronization approach between two initial-dependent electomotors. In the case of network synchronization and pattern selection, a chain network is designed and statistical factor of synchronization is calculated to predict the synchronization stability on the network. It is found that the synchronization stability shows some dependence on initial setting for one variable(external load). The Hamilton energy is also calculated to find the behavior dependence on initial setting and parameter selection by using Helmholtz theorem.