Contraction theory based synchronization analysis of impulsively coupled oscillators

Abstract

Impulsively coupled oscillators which are assumed to interact with each other only at discrete times have many applications in practice. In this paper, we introduce the concept of partial contraction theory of impulsive systems, which is used to investigate the synchronization problem of impulsively coupled oscillators. Contraction analysis of two impulsively coupled oscillators and networked impulsively coupled oscillators is provided, respectively. Very simple but very general results for synchronization of impulsively coupled oscillators are derived. Numerical simulations show the effectiveness of our theoretical results.

Anti-phase synchronization and symmetry-breaking bifurcation of impulsively coupled oscillators

“…[18][19][20][21]). Han et al [18] studied a class of impulsively coupled complex dynamical systems and established several criteria regarding to the eigenvalues and the eigenvectors of the coupling matrix for synchronization of such systems.…”

“…Yang et al studied a class of impulsively coupled complex switched networks and their robust synchronization in terms of parametric uncertainties and time-varying delays in [19]. Jiang and Bi introduced the concept of partial contraction theory of impulsive systems and investigated the synchronization problem of impulsively coupled oscillators in [20]. Jiang et al [21] studied the complex dynamics of a non-smooth system which was unidirectionally impulsively coupled by three Duffing oscillators in a ring structure.…”

Complex dynamics analysis of impulsively coupled Duffing oscillators with ring structure

“…Very recently, impulsively coupled oscillators that are assumed to interact with each other only at discrete times have drawn considerable attention. [12][13][14][15][16] Pulse coupled neural networks which are special impulsively coupled oscillators have been utilized for various image processing applications, including image segmentation, feature generation, face extraction, motion detection, and so on. [12,13] In Ref.…”

“…In Ref. [16], the authors introduced the concept of partial contraction theory of impulsive systems and investigated the synchronization problem of impulsively coupled oscillators. On the other hand, networked dynamical systems can achieve synchronization without interacting with each other continuously.…”