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Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
We study the evolution of heterogeneous networks of oscillators subject to a state-dependent interconnection rule. We find that heterogeneity in the node dynamics is key in organizing the architecture of the functional emerging networks. We…
Real-world networks in technology, engineering and biology often exhibit dynamics that cannot be adequately reproduced using network models given by smooth dynamical systems and a fixed network topology. Asynchronous networks give a…
In this article, we analyze a nonlocal ring network of adaptively coupled phase oscillators. We observe a variety of frequency-synchronized states such as phase-locked, multicluster and solitary states. For an important subclass of the…
The stability of synchronised networked systems is a multi-faceted challenge for many natural and technological fields, from cardiac and neuronal tissue pacemakers to power grids. In the latter case, the ongoing transition to distributed…
Synchronization is essential for proper functioning of the power grid. We investigate the synchronous state and its stability for a network with a cyclic topology and with the evolution of the states satisfying the swing equations. We…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
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…
Abrupt changes of behaviour in complex networks can be triggered by a single node. This work describes the dynamical fundamentals of how the behaviour of one node affects the whole network formed by coupled phase-oscillators with…
Oscillatory synchrony is hypothesized to support the flow of information between brain regions, with different phase-locked configurations enabling activation of different effective interactions. Along these lines, past work has proposed…
Oscillator networks found in social and biological systems are characterized by the presence of wide ranges of coupling strengths and complex organization. Yet robustness and synchronization of oscillations are found to emerge on…
There is enormous interest -- both mathematically and in diverse applications -- in understanding the dynamics of coupled oscillator networks. The real-world motivation of such networks arises from studies of the brain, the heart, ecology,…
We study the collective dynamics of oscillator networks with phase-repulsive coupling, considering various network sizes and topologies. The notion of link frustration is introduced to characterize and quantify the network dynamical states.…
Weakly coupled oscillators are used throughout the physical sciences, particularly in mathematical neuroscience to describe the interaction of neurons in the brain. Systems of weakly coupled oscillators have a well-known decomposition to a…
Real-world systems in epidemiology, social sciences, power transportation, economics and engineering are often described as multilayer networks. Here we first define and compute the symmetries of multilayer networks, and then study the…
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…
The collective behavior of the ensembles of coupled nonlinear oscillator is one of the most interesting and important problems in modern nonlinear dynamics. In this paper, we study rotational dynamics, in particular space-time structures,…
The study of the interplay between the structure and dynamics of complex multilevel systems is a pressing challenge nowadays. In this paper, we use a semi-annealed approximation to study the stability properties of Random Boolean Networks…
Complex network dynamics have been analyzed with models of systems of coupled switches or systems of coupled oscillators. However, many complex systems are composed of components with diverse dynamics whose interactions drive the system's…
Coupled oscillator networks often display transitions between qualitatively different phase-locked solutions -- such as synchrony and rotating wave solutions -- following perturbation or parameter variation. In the limit of weak coupling,…