Related papers: Complex behavior in chains of nonlinear oscillator…
We study a triangular network of three populations of coupled phase oscillators with identical frequencies. The populations interact nonlocally, in the sense that all oscillators are coupled to one another, but more weakly to those in…
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…
We study the spatio-temporal dynamics of a model of polar active fluid in two dimensions. The system exhibits a transition from an isotropic to a polarized state as a function of density. The uniform polarized state is, however, unstable…
We study an unusual but robust phenomenon that appears in an example system of four coupled phase oscillators. We show that the system can have a robust attractor that responds to a specific detuning between certain pairs of the oscillators…
We measure stretched exponential behavior, exp(- (t/t_0)**beta), over many decades in a one-dimensional array of coupled chaotic electronic elements just above a crisis-induced intermittency transition. There is strong spatial heterogeneity…
Chimera states are dynamical patterns in networks of coupled oscillators in which regions of synchronous and asynchronous oscillation coexist. Although these states are typically observed in large ensembles of oscillators and analyzed in…
Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale…
The identification of the limiting factors in the dynamical behavior of complex systems is an important interdisciplinary problem which often can be traced to the spectral properties of an underlying network. By deriving a general relation…
We study a simple dynamical model exhibiting sequential dynamics. We show that in this model there exist sets of parameter values for which a cyclic chain of saddle equilibria, $O_k$, $k=1, \ldots, p$, have two dimensional unstable…
We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become…
The ability to reliably predict critical transitions in dynamical systems is a long-standing goal of diverse scientific communities. Previous work focused on early warning signals related to local bifurcations (critical slowing down) and…
Optomechanical systems are known to exhibit a rich set of complex dynamical features including various types of chaotic behavior and multi-stability. Although this exotic behavior has attracted an intense research interest, the utilization…
Nonlinear phenomena including multiple equilibria and spontaneous oscillations are common in fluid networks containing either multiple phases or constituent flows. In many systems, such behavior might be attributed to the complicated…
We report on a self-emerging chimera state in a homogeneous chain of nonlocally and nonlinearly coupled oscillators. This chimera, i.e. a state with coexisting regions of complete and partial synchrony, emerges via a supercritical…
Non-reciprocal interactions are a defining feature of many complex systems, biological, ecological, and technological, often pushing them far from equilibrium and enabling rich dynamical responses. These asymmetries can arise at multiple…
Complex network theory provides a unifying framework for the study of structured dynamic systems. The current literature emphasizes a widely reported phenomenon of intermittent interaction among network vertices. In this paper, we introduce…
Nonautonomous driving of an oscillator has been shown to enlarge the Arnold tongue in parameter space, but little is known about the analogous effect for a network of oscillators. To test the hypothesis that deterministic nonautonomous…
Here we numerically study a model of excitable media, namely, a network with occasionally quiet nodes and connection weights that vary with activity on a short-time scale. Even in the absence of stimuli, this exhibits unstable dynamics,…
The tools of weakly coupled phase oscillator theory have had a profound impact on the neuroscience community, providing insight into a variety of network behaviours ranging from central pattern generation to synchronisation, as well as…
Large-scale collective oscillation is discovered in the two-dimensional Euler equations. For initial conditions far from a base stationary flow, the system does not relax to the base stationary flow, but instead shows pairs of coherent…