Crowd synchrony in chaotic oscillators

Quorum sensing is a phenomenon wherein the size of an ensemble (population density) decides its dynamical state. This happens when its constituting elements alter their dynamics coherently with the change in their population. In case of chaotic ensemble, as a precursor to the emergence of global chaotic synchronization, the chaotic elements undergo various dynamical transitions (chaotic state →\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document} silent/periodic state →\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document} periodic state/ intermittent chaos →\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document} chaotic state) sequentially with the increase in their population. Among these sequence of quorum transitions, we mark the transition periodic state/intermittent chaos →\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$\rightarrow $$\end{document} chaotic state (i.e the final quorum transition between the unsynchronized and synchronized chaotic states) as a ‘crowd synchrony’ transition for convenience. In contrast to the conventional quorum sensing mechanism, we study this population-based phenomenon by exploring the scenario wherein the chaotic elements interact via an element (of same kind) resting in a steady state, i.e the surrounding of the elements is not only dynamic but also incorporates the underlying features of the elements. Apart from the other advantages (discussed in the text), considering the surrounding of the elements as an element, resolves the issue regarding the dimensionality of the surround (which has not been addressed before) when more than one interacting species are involved. The proposed mechanism has been tested on two different class of chaotic oscillators: spiking neuron (i.e a relaxed biological oscillator) and Chua’s circuit, i.e a sinusoidal-type electrical oscillator (for the experimental verification).