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Multiplicity of phase states within frequency locked bands in periodically forced oscillatory systems may give rise to front structures separating states with different phases. A new front instability is found within bands where…
The dynamics of mixedness and entanglement is examined by solving the time-dependent Schr\"{o}dinger equation for three coupled harmonic oscillator system with arbitrary time-dependent frequency and coupling constants parameters. We assume…
The model of coupled oscillators plays an important role in modern physics. It is used for description of various processes: from vibrations atoms in solid states to electromagnetic oscillations in slow-wave structures. The model with…
We propose an approach for inferring strength of coupling between two systems from their transient dynamics. This is of vital importance in cases where most information is carried by the transients, for instance in evoked potentials…
Synchronization in a frequency-weighted Kuramoto model with a uniform frequency distribution is studied. We plot the bifurcation diagram and identify the asymptotic coherent states. Numerical simulations show that the system undergoes two…
We study when a network of coupled oscillators with inertia ceases to follow a time-dependent driving protocol coherently, using a simplified graph-based model motivated by inverter-dominated energy systems. We show that this loss of…
We propose a coupled system of fast and slow phase oscillators. We observe two-step transitions to quasi-periodic motions by direct numerical simulations of this coupled oscillator system. A low-dimensional equation for order parameters is…
An ensemble of uncoupled limit-cycle oscillators receiving common Poisson impulses shows a range of non-trivial behavior, from synchronization, desynchronization, to clustering. The group behavior that arises in the ensemble can be…
The enigmatic stability of population oscillations within ecological systems is analyzed. The underlying mechanism is presented in the framework of two interacting species free to migrate between two spatial patches. It is shown that that…
The emergence of rich dynamical phenomena in coupled self-sustained oscillators, primarily synchronization and amplitude death, has attracted considerable interest in several fields of science and engineering. Here, we present a…
Networks of coupled nonlinear oscillators can display a wide range of emergent behaviours under variation of the strength of the coupling. Network equations for pairs of coupled oscillators where the dynamics of each node is described by…
Synchronization, which is caused by mutual coupling, and turnover, which is the replacement of old components with new ones, are observed in various open systems consisting of many components. Although these phenomena can co-occur, the…
We study the dissipative dynamics of a two-level system under ultrastrong driving when the frequency and strength of the exciting field exceed significantly the transition frequency. We find three qualitatively different regimes of such…
The mechanism of synchronization of oscillations in two identical coupled flow systems has beenstudied. The time (past the coupling onset) during which a synchronous oscillation regime is establisheddepends on the oscillation phase…
Two decades ago, a phenomenon resembling Landau damping was described in the synchronization of globally coupled oscillators: the evidence of a regime where the order parameter decays when linear theory predicts neutral stability for the…
We examine examples of weakly nonlinear systems whose steady states undergo a bifurcation with increasing forcing, such that a forced subsystem abruptly ceases to absorb additional energy, instead diverting it into an initially quiescent,…
Experiments are carried out with a globally coupled, externally forced population of limit-cycle electrochemical oscillators with an approximately unimodal distribution of heterogeneities. Global coupling induces mutually entrained (at…
Many real oscillators are coupled to other oscillators and the coupling can affect the response of the oscillators to stimuli. We investigate phase response curves (PRCs) of coupled oscillators. The PRCs for two weakly coupled phase-locked…
We revisit the mean field model of globally and harmonically coupled parametric oscillators subject to periodic block pulses with initially random phases. The phase diagram of regions of collective parametric instability is presented, as is…
The dynamics of a non-autonomous oscillator in which the phase and frequency of the external force depend on the dynamical variable is studied. Such a control of the phase and frequency of the external force leads to the appearance of…