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Collective behavior in large ensembles of dynamical units with non-pairwise interactions may play an important role in several systems ranging from brain function to social networks. Despite recent work pointing to simplicial structure,…
We study synchronization dynamics in populations of coupled phase oscillators with higher-order interactions and community structure. We find that the combination of these two properties gives rise to a number of states unsupported by…
We investigate dynamics and bifurcations in a mathematical model that captures electrochemical experiments on arrays of microelectrodes. In isolation, each individual microelectrode is described by a one-dimensional unit with a bistable…
We study a system of coupled phase oscillators near a saddle-node on an invariant circle bifurcation and driven by random intrinsic frequencies. Under the variation of control parameters, the system undergoes a phase transition changing the…
The ubiquitous occurrence of cluster patterns in nature still lacks a comprehensive understanding. It is known that the dynamics of many such natural systems is captured by ensembles of Stuart-Landau oscillators. Here, we investigate…
Cluster synchronization is a fundamental phenomenon in systems of coupled oscillators. Here, we investigate clustering patterns that emerge in a unidirectional ring of four delay-coupled electrochemical oscillators. A voltage parameter in…
We study the phenomenon of cluster synchrony that occurs in ensembles of coupled phase oscillators when higher-order modes dominate the coupling between oscillators. For the first time, we develop a complete analytic description of the…
We reduce the dynamics of an ensemble of mean-coupled Stuart-Landau oscillators close to the synchronized solution. In particular, we map the system onto the center manifold of the Benjamin-Feir instability, the bifurcation destabilizing…
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…
Ordered and disordered behavior in large ensembles of coupled oscillators map to different functional states in a wide range of applications, e.g., active and resting states in the brain and stable and unstable power grid configurations.…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
The apparent stability of population oscillations in ecological systems is a long-standing puzzle. A generic solution for this problem is suggested here. The stabilizing mechanism involves the combined effect of spatial migration,…
We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with…
We analyze the collective dynamics of an ensemble of globally coupled, externally forced, identical mechanical oscillators with cubic nonlinearity. Focus is put on solutions where the ensemble splits into two internally synchronized…
This paper presents a stability analysis of simple neuromodules displaying fold bifurcations (leading to hysteresis), flip bifurcations (period doubling and undoubling to and from chaos) and Neimark-Sacker bifurcations (quasiperiodic and…
We study a system of dynamical units, each of which shows excitable or oscillatory behavior, depending on the choice of parameters. When we couple these units with repressive bonds, we can control the duration of collective oscillations for…
The behaviors of coupled oscillators, each of which has periodic motion with random natural frequency in the absence of coupling, are investigated. Some novel collective phenomena are revealed. At the onset of instability of the…
Fast-slow dynamical systems have subsystems that evolve on vastly different timescales, and bifurcations in such systems can arise due to changes in any or all subsystems. We classify bifurcations of the critical set (the equilibria of the…
Synchronization processes play critical roles in the functionality of a wide range of both natural and man-made systems. Recent work in physics and neuroscience highlights the importance of higher-order interactions between dynamical units,…
Recent experiments have highlighted how collective dynamics in networks of brain regions affect behavior and cognitive function. In this paper we show that a simple, homogeneous system of densely connected oscillators representing the…