Related papers: Controlled Perturbation-Induced Switching in Pulse…
The control of complex systems and network-coupled dynamical systems is a topic of vital theoretical importance in mathematics and physics with a wide range of applications in engineering and various other sciences. Motivated by recent…
Being permanently confronted with an uncertain world, brains have faced evolutionary pressure to represent this uncertainty in order to respond appropriately. Often, this requires visiting multiple interpretations of the available…
We show that peculiar collective dynamics called slow switching arises in a population of leaky integrate-and-fire oscillators with delayed, all-to-all pulse-couplings. By considering the stability of cluster states and symmetry possessed…
Populations of flashing fireflies, claps of applauding audience, cells of cardiac and circadian pacemakers reach synchrony via event-triggered interactions, referred to as pulse couplings. Synchronization via pulse coupling is widely used…
Random networks of symmetrically coupled, excitable elements can self-organize into coherently oscillating states if the networks contain loops (indeed loops are abundant in random networks) and if the initial conditions are sufficiently…
Coupled parametric oscillators were recently employed as simulators of artificial Ising networks, with the potential to solve computationally hard minimization problems. We demonstrate a new dynamical regime within the simplest network -…
Although the set of permutation symmetries of a complex network can be very large, few of the symmetries give rise to stable synchronous patterns. Here we present a new framework and develop techniques for controlling synchronization…
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator…
Systems of $N$ identical globally coupled phase oscillators can demonstrate a multitude of complex behaviours. Such systems can have chaotic dynamics for $N>4$ when a coupling function is biharmonic. The case $N = 4$ does not possess…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
A single neuron is known to generate almost identical spike trains when the same fluctuating input is repeatedly applied. Here, we study the reliability of spike firing in a pulse-coupled network of oscillator neurons receiving fluctuating…
For general networks of pulse-coupled oscillators, including regular, random, and more complex networks, we develop an exact stability analysis of synchronous states. As opposed to conventional stability analysis, here stability is…
An ensemble of pulse-coupled phase-oscillators is thoroughly analysed in the presence of a mean-field coupling and a dispersion of their natural frequencies. In spite of the analogies with the Kuramoto setup, a much richer scenario is…
Oscillators coupled in a network can synchronize with each other to yield a coherent population rhythm. If multiple such networks are coupled together, the question arises whether these rhythms will synchronize. We investigate the impact of…
Cluster synchronization in synthetic networks of coupled chaotic oscillators is investigated. It is found that despite the asymmetric nature of the network structure, a subset of the oscillators can be synchronized as a cluster while the…
Following the long-lived qualitative-dynamics tradition of explaining behavior in complex systems via the architecture of their attractors and basins, we investigate the patterns of switching between qualitatively distinct trajectories in a…
Motivated by the aim to find new medical strategies to suppress undesirable neural synchronization we study the control of oscillations in a system of inhibitory coupled noisy oscillators. Using dynamical properties of inhibition, we find…
A network of propagating nonlinear oscillatory modes (waves) in the human brain is shown to generate collectively synchronized spiking activity (hypersynchronous spiking) when both amplitude and phase coupling between modes are taken into…
We report a transition from asynchronous to oscillatory behaviour in balanced inhibitory networks for class I and II neurons with instantaneous synapses. Collective oscillations emerge for sufficiently connected networks. Their origin is…
Sufficient conditions for complete controllability of $N$-level quantum systems subject to a single control pulse that addresses multiple allowed transitions concurrently are established. The results are applied in particular to Morse and…