Itinerant chimeras in an adaptive network of pulse-coupled oscillators

Abstract

In a network of pulse-coupled oscillators with adaptive coupling, we discover a novel dynamical regime which we call an "itinerant chimera". Similarly as in classical chimera states, the network splits into two domains, the coherent and the incoherent ones. The drastic difference is that the composition of the domains is volatile, i.e. the oscillators demonstrate spontaneous switching between the domains. This process can be seen as traveling of the oscillators from one domain to another, or as traveling of the chimera core across the network. We explore the basic features of the itinerant chimeras, such as the mean and the variance of the core size, and the oscillators lifetime within the core. We also study the scaling behavior of the system and show that the observed regime is not a finite-size effect but a key feature of the collective dynamics which persists even in large networks.

Patterns of Synchrony in Complex Networks of Adaptively Coupled Oscillators

“…In fact, due to the co-stability with splay type multiclusters, mix type multicluster states are very unlikely to find from uniformly distributed random initial conditions. In previous studies mix type multiclusters have not even been mentioned [KAS19]. In order to find these particular states, we used specially prepared initial condition motivated by the results described in Section 5.5.…”

Integrative Models of Brain Structure and Dynamics: Concepts, Challenges, and Methods

“…In a metastable system, the elements show transiently fixed relationship with each other (e.g., transiently synchronized activations of neural populations in the brain). Coexistence of synchronized and desynchronized behaviors in a system of interacting oscillators is an indication of its metastable nature (Shanahan, 2010;Kasatkin et al, 2019). Importantly, such behaviors are shortlived, and the system endogenously transitions between different attractor (synchronized) states, whose basins of attractions can be arbitrarily close in the phase space (Tsuda, 2009).…”

“…Metastability is believed to be a necessary physical property underlying the coordinated dynamics of spatially distributed neuronal populations in the brain (Fingelkurts and Fingelkurts, 2004;Freeman and Holmes, 2005). Metastability in a system of interacting oscillators can be quantified by using the oscillators' instantaneous phases as variables of coordination (Shanahan, 2010;Tognoli and Kelso, 2014;Kasatkin et al, 2019;Venkadesh et al, 2020; Figure 1E). Spatiotemporal recordings of neural activity obtained from EEG and MEG, owing to their resolvability of high frequency oscillations such as gamma frequency bands (Figure 1B), allow for an interpretation of mesoscopic transitory dynamics using the framework of metastability (Freeman and Holmes, 2005).…”

“…Using Kuramoto oscillators, Schmidt et al (2015) showed that the high-degree hub regions in the brain anatomical connectivity (van den Heuvel and Sporns, 2011) synchronized at a higher level than other regions and were also crucial in achieving intermodular synchronization. Similarly, pulsecoupled phase oscillators have been simulated using a fully-connected network with synaptic plasticity (Kasatkin et al, 2019). Here, oscillators self-organized into multiple volatile domains of synchronized and desynchronized activity called itinerant chimeras, a special case of metastability.…”

Birth and Stabilization of Phase Clusters by Multiplexing of Adaptive Networks

“…Various synchronization patterns are known, like cluster synchronization where the network splits into groups of synchronous elements [14], or partial synchronization patterns like chimera states where the system splits into coexisting domains of coherent (synchronized) and incoherent (desynchronized) states [15][16][17]. These patterns were also explored in adaptive networks [18][19][20][21][22][23][24][25][26][27][28][29][30][31][32][33]. Furthermore, adapting the network topology has also successfully been used to control cluster synchronization in delay-coupled networks [34].Another focus of recent research in network science are multilayer networks, which are systems interconnected through different types of links [35][36][37][38].…”