Complex spatiotemporal dynamics in a network of locally and magnetically coupled VDPCL oscillators

Abstract

Nowadays, we are witnessing a dramatic advance in wireless technology-based magnetic induction. It is used both for wireless power transfer and data transfer between systems. In addition, it is widely shown that a network of coupled identical oscillators exhibits complex collective behavior characterized by the coexistence of coherent and incoherent domains and termed as chimera state. In this paper, we consider a network of (N ≥10) locally and magnetically coupled Van der Pol oscillators coupled to a linear circuit (VDPCL oscillators). We then investigate the different arrangements of their interactions in terms of the magnetic coupling coefficients, taken as the bifurcation parameters. Statistical measure namely the strength of incoherence is used to classify the synchronized states in the network. Another algorithm described in the text is used for the classification and is consistent with the strength of incoherence. Numerical simulation reveals that the emerging spatiotemporal behaviors depend on the choice of initial conditions revealing the presence of multistability in the network. This network configuration also reveals a rich repertoire of spatiotemporal dynamics such as coherence/global synchronization, decoherence, chimera state, cluster synchronization, and solitary states as the magnetic coupling coefficients vary. Some other interesting behaviors such as traveling clustered wave, double and multicluster chimera state, and clustered solitary state for a specific set of initial conditions are also obtained. Furthermore, Pspice-based simulations carried out for a network of (N=10) oscillators are consistent with the numerical simulations based on the mathematical model.