Symmetry breaking dynamics induced by mean-field density and low-pass filter

Abstract

The phenomenon of spontaneous symmetry breaking facilitates the onset of a plethora of nontrivial dynamical states/patterns in a wide variety of dynamical systems. Spontaneous symmetry breaking results in amplitude and phase variations in a coupled identical oscillator due to the breaking of the prevailing permutational/translational symmetry of the coupled system. Nevertheless, the role and the competing interaction of the low-pass filter and the mean-field density parameter on the symmetry breaking dynamical states are unclear and yet to be explored explicitly. The effect of low pass filtering along with the mean-field parameter is explored in conjugately coupled Stuart–Landau oscillators. The dynamical transitions are examined via bifurcation analysis. We show the emergence of a spontaneous symmetry breaking (asymmetric) oscillatory state, which coexists with a nontrivial amplitude death state. Through the basin of attraction, the multi-stable nature of the spontaneous symmetry breaking state is examined, which reveals that the asymmetric distribution of the initial state favors the spontaneous symmetry breaking dynamics, while the symmetric distribution of initial states gives rise to the nontrivial amplitude death state. In addition, the trade-off between the cut-off frequency of the low-pass filter along with the mean-field density induces and enhances the symmetry breaking dynamical states. Global dynamical transitions are discussed as a function of various system parameters. Analytical stability curves corresponding to the nontrivial amplitude death and oscillation death states are deduced.

Additional complex conjugate feedback-induced explosive death and multistabilities

“…Recent investigations reveal that appropriate feedback can restore oscillatory dynamics or induce the oscillation death state depending on the properties of the ensembles, coupling architecture, and the kind of feedback and its strength [11][12][13]. Importantly, among the various intrinsic and extrinsic parameters such as time-delay, low-pass filtering, mean-field density, etc., typically, the feedback is used for controlling purposes [14][15][16][17][18][19][20][21][22]. For instance, the conjugate feedback or the selffeedback approach is used for controlling the birhythmicity in different realistic models such as energy harvesting systems as well as biochemical systems [23,24].…”

Emergence of multistability and strongly asymmetric collective modes in two quorum sensing coupled identical ring oscillators

“…Very recently [17] it has been shown that the indirectly and conjugately mean-field coupled Stuart-Landau oscillators demonstrate the emergence of a spontaneous symmetry breaking oscillatory state, which coexists with a nontrivial amplitude death state. Indirect coupling is realized via the addition of low-pass filter with the parameter named "the mean-field density", which can be considered as a version of the quorum sensing mechanism.…”