Spatiotemporal patterns in a network of locally and magnetically coupled VDPCL oscillators

Recent advancements in wireless magnetic induction technology have enabled applications in both wireless power and data transfer. This study investigates the spatiotemporal dynamics of a network of N >= 10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{N}}\ge 10$$\end{document} magnetically coupled VDPCL oscillator (Van der Pol oscillator coupled to linear circuit). The focus is on exploring these dynamics based on magnetic coupling coefficients. Using statistical measures namely the strength of incoherence, the cross-correlation coefficient, and a classification algorithm described in the text, synchronized states within the network are categorized. Numerical simulations reveal diverse dynamics, including coherence, incoherence, chimera states, solitary states, and multicluster behaviors, influenced by initial conditions and magnetic coefficients. Also, specific dynamics such as solitary at the cluster state, clustered solitary state and water-like traveling cluster waves are obtained. These phenomena contribute to a richer understanding of the complex dynamics emerging in magnetically coupled oscillator networks. To validate our findings, PSPICE-based circuit simulations are performed for N=10\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$${\varvec{N}}=10$$\end{document} oscillators aligning well with the predictions of mathematical models. This study not only sheds light on the diverse dynamics achievable in magnetically coupled oscillator networks but also holds implications for advancing wireless technologies. The systematic classification and validation through PSPICE simulations contribute to the robustness of our findings and their applicability in practical scenarios.