Multifaceted Dynamics of Janus Oscillator Networks

Abstract

Recent research has led to the discovery of fundamental new phenomena in network synchronization, including chimera states, explosive synchronization, and asymmetry-induced synchronization. Each of these phenomena has thus far been observed only in systems designed to exhibit that one phenomenon, which raises the questions of whether they are mutually compatible and, if so, under what conditions they co-occur. Here, we introduce a class of remarkably simple oscillator networks that concurrently exhibit all of these phenomena. The dynamical units consist of pairs of nonidentical phase oscillators, which we refer to as Janus oscillators by analogy with Janus particles and the mythological figure from which their name is derived. In contrast to previous studies, these networks exhibit (i) explosive synchronization with identical oscillators; (ii) extreme multistability of chimera states, including traveling, intermittent, and bouncing chimeras; and (iii) asymmetryinduced synchronization in which synchronization is promoted by random oscillator heterogeneity. These networks also exhibit the previously unobserved possibility of inverted synchronization transitions, in which a transition to a more synchronous state is induced by a reduction rather than an increase in the coupling strength. These various phenomena are shown to emerge under rather parsimonious conditions, and even in locally connected ring topologies, which has the potential to facilitate their use to control and manipulate synchronization in experiments.

Collective dynamics of random Janus oscillator networks

“…By employing the scheme provided by the OA ansatz, we obtained, for random regular networks, a reduced set of equations whereby critical points of the dynamics were revealed. We found that several collective behaviors coexist for intermediate coupling values, elucidating the findings in [6]. Although initially obtained for homogeneous networks, we verified that the solutions of the reduced system fitted ac-curately numerical experiments for dense ER networks.…”

“…All in all, we provided the first theoretical and numerical analysis of ensembles of Janus oscillators on homogeneous and heterogeneous random networks. As such, our work raises further interesting questions about the study initiated by Nicolaou et al [6]. For instance, future investigations should target the dynamics on sparse and correlated networks -situations in which the ensemble approach in [10] and mean-field techniques are inaccurate in predicting tipping points of the system -as well as limitations of the OA manifold in capturing the Janus dynamics.…”

“…In all these cases, phase oscillator models had to be specially designed so that those non-trivial states could be scrutinized. Very recently, however, Nicolaou et al [6] defined an oscillator model coined as Janus oscillators; the name is inspired in the homonym two-faced god of Roman mythology and reflects the two-dimensional character of an isolated oscillator -each "face" of a Janus unit consists of a Kuramoto oscillator, whose natural frequency has the same absolute value but opposite sign to the frequency of its counter-face. When coupled on one-dimensional regular graphs, Janus oscillators have been found to exhibit a striking rich dynamical behavior that encompasses the co-occurrence of several dynamical patterns, in spite of the simplicity of the topology and the oscillator model itself [6].The Janus model was introduced as a potential model for biological systems such as the Chlamydomonas cells with counterrotating flagella [7,8].…”

The Cyborg Philharmonic: Synchronizing interactive musical performances between humans and machines

“…A natural direction of future work would involve studying the effects of more recent synchronization techniques like Janus oscillators (Nicolaou et al, 2019) shown to concurrently handle phenomena like network synchronization and asymmetry-induced synchronization for scenarios with (a) explosive synchronizations and (b) extreme multi-stability of chimaera states. Further, use of Quantum Neural Networks (Narayanan and Menneer, 2000) might provide enhanced predictive power for better leader-follower estimation in our architecture.…”

A review of swarmalators and their potential in bio-inspired computing

“…Equipping swarmalators with these features would likely cure the poverty of phenomena in the first, third, and fourth quadrants of the (J, K) plane ( Figure 2) and produce new dynamics in Iswasa-tanaka and Vicesek type models, too. Phase models more sophisticated than the Kuramoto model could also be explored; the Winfree model [94] or the newly introduced Janus oscillators [95] would be exciting to experiment with. Swarmalators with discrete and spatially local coupling also merit study and are useful in com-puter and communication systems.…”