Synchronization and anti-synchronization of chaos for a multi-degree-of-freedom dynamical system by control of velocity

Abstract

For multi-degree-of-freedom dynamical systems, a novel control method was proposed to realize synchronization and anti-synchronization of chaos between the original and derived systems. The presented method was proved theoretically and realized by linear coupling of velocity. Furthermore, for any coupling coefficient larger than the critical value, the two systems can continue synchronization and anti-synchronization by the coupling method. This means that the synchronization and anti-synchronization can be kept within a wide range of coupling parameters. The simulation results for Duffing and Mathieu systems proved that the proposed method was correct and effective.

Dynamic system with no equilibrium and its chaos anti-synchronization

“…It is noted that anti-synchronization is an attractive scheme, where two dynamical systems are synchronized in amplitude, but with opposite sign [57][58][59]. Anti-synchronization was applied in different areas, for example temporal pattern recognition [60], memristive neural network [61], multi-degree-of-freedom dynamical system [62], security communication [63] and coupled systems [64,65]. Motivated by the fact that chaos anti-synchronization phenomena are of fundamental importance in the study of dynamical systems, in this section, the antisynchronization of two non-equilibrium systems (master and slave ones) is reported.…”

Anti-Synchronization and Synchronization of Coupled Chaotic System With Ring Connection and Stochastic Perturbations

“…In [18], the two systems can be obtained synchronization and anti-synchronization by the coupling method. In [19], [20], the authors investigate the complete synchronization and anti-synchronization behavior in an array of coupled chaotic systems with ring connection.…”

Adaptive observer-based synchronization of two non-identical chaotic systems with unknown parameters

“…The same problem for the stochastic chaotic systems has been investigated in Salarieh and Shahrokhi, (2008) and Zhao (2012). Alongside the theoretical part, many studies have been also conducted regarding applications of synchronization of chaotic systems (Wei and Wang, 2013;Qin et al, 2014). In practice, usually all system states are not available.…”