Recurrence analysis and synchronization of two resistively coupled Duffing-type oscillators

In this work, we study the complex dynamics and synchronization of two coupled Duffing-type circuits within the framework of recurrence quantification analysis (RQA). For the case of a Duffing oscillator driven by a sinusoidal voltage source, the behavior of various RQA parameters has been shown to reveal complex chaotic transitions taking place in its oscillatory behavior as the amplitude of forcing term is varied. The problem of synchronization of two identical Duffing oscillators coupled together resistively is further investigated using RQA. The simulated recurrence plot (RP) and plot for the τ\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\tau $$\end{document}-recurrence/recurrence probability, p(τ)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$p(\tau )$$\end{document}, have been used extensively over different control parameter regime to understand the dynamical complexity including chaos synchronization for both one-way and two-way coupled Duffing-type oscillators. The critical parameter beyond which chaos synchronization occurs in such systems is determined.