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The phenomenon of explosive synchronization, which originates from hypersensitivity to small perturbation caused by some form of frustration prevailed in various physical and biological systems, has been shown to lead events of cascading…

We study the onset of synchronization in lattices of limit cycle oscillators with long-range coupling by means of numerical simulations. In this regime the critical coupling strength depends on the system size and interaction range…

The conditions under which synchronization is achieved for a one-dimensional ring of identical phase oscillators with Kuramoto-like local coupling are studied. The system is approached in the weakly coupled approximation as phase units.…

In a many body system, constituents interact with each other, forming a recursive pattern of interaction and giving rise to many interesting phenomena. Based upon concepts of the modern many body theory, a model for a generic many body…

Cognitive function is driven by dynamic interactions between large-scale neural circuits or networks, enabling behavior. Fundamental principles constraining these dynamic network processes have remained elusive. Here we use network control…

The synchronization stability of a complex network system of coupled phase oscillators is discussed. In case the network is affected by disturbances, a stochastic linearized system of the coupled phase oscillators may be used to determine…

The connectivity of individual neurons of large neural networks determine both the steady state activity of the network and its answer to external stimulus. Highly diluted random networks have zero activity. We show that increasing the…

Neuronal networks constitute a special class of dynamical systems, as they are formed by individual geometrical components, namely the neurons. In the existing literature, relatively little attention has been given to the influence of…

Propagation of oscillatory signals through the cortex and coherence is shaped by the connectivity structure of neuronal circuits. This study systematically investigates the network and stimulus properties that shape network responses. The…

Most real-world networks exhibit a significant degree of modularity. Understanding the effects of such topology on dynamical processes is pivotal for advances in social and natural sciences. In this work we consider the dynamics of Kuramoto…

Synchronized neural spiking is associated with many cognitive functions and thus, merits study for its own sake. The analysis of neural synchronization naturally leads to the study of repetitive spiking and consequently to the analysis of…

Coupled oscillator networks provide mathematical models for interacting periodic processes. If the coupling is weak, phase reduction -- the reduction of the dynamics onto an invariant torus -- captures the emergence of collective dynamical…

A class of adaptation functions is found for which a synchronous oscillation mode exists in the network of phase oscillators with triadic couplings. It is shown that the destruction of the synchronous mode occurs differently for networks…

We consider a mean-field model of coupled phase oscillators with quenched disorder in the coupling strengths and natural frequencies. When these two kinds of disorder are uncorrelated (and when the positive and negative couplings are equal…

The understanding of synchronization ranging from natural to social systems has driven the interests of scientists from different disciplines. Here, we have investigated the synchronization dynamics of the Kuramoto dynamics departing from…

The brain is in a state of perpetual reverberant neural activity, even in the absence of specific tasks or stimuli. Shedding light on the origin and functional significance of such a dynamical state is essential to understanding how the…

We try to design a quantum neural network with qubits instead of classical neurons with deterministic states, and also with quantum operators replacing teh classical action potentials. With our choice of gates interconnecting teh neural…

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 consider the problem of synchronization of coupled oscillators in a Kuramoto-type model with lossy couplings. Kuramoto models have been used to gain insight on the stability of power networks which are usually nonlinear and involve large…

We study the phase-synchronization properties of systolic and diastolic arterial pressure in healthy subjects. We find that delays in the oscillatory components of the time series depend on the frequency bands that are considered, in…