Related papers: Amplitude and phase dynamics in oscillators with d…
In a network of nonlocally coupled Stuart-Landau oscillators with symmetry-breaking coupling, we study numerically, and explain analytically, a family of inhomogeneous steady states (oscillation death). They exhibit multi-cluster patterns,…
We introduce a general mechanism for amplitude death in coupled synchronizable dynamical systems. It is known that when two systems are coupled directly, they can synchronize under suitable conditions. When an indirect feedback coupling…
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…
We analyze an intermediate collective regime where amplitude oscillators distribute themselves along a closed, smooth, time-dependent curve $\mathcal{C}$, thereby maintaining the typical ordering of (identical) phase oscillators. This is…
Recently, the explosive phase transitions, such as explosive percolation and explosive synchronization, have attracted extensive research interest. So far, most existing works investigate Kuramoto-type models, where only phase variables are…
When nonlinear dynamical systems are coupled, depending on the intrinsic dynamics and the manner in which the coupling is organized, a host of novel phenomena can arise. In this context, an important emergent phenomenon is the complete…
Coupled oscillators with time-delayed network interactions are critical to understand synchronization phenomena in many physical systems. Phase reductions to finite-dimensional phase oscillator networks allow for their explicit analysis.…
We consider networks of delay-coupled Stuart-Landau oscillators. In these systems, the coupling phase has been found to be a crucial control parameter. By proper choice of this parameter one can switch between different synchronous…
We report the emergence of stable amplitude chimeras and chimera death in a two-layer network where one layer has an ensemble of identical nonlinear oscillators interacting directly through local coupling and indirectly through dynamic…
In this article, we propose a very efficient technique to enhance the dynamical robustness for a network of mean-field coupled oscillators experiencing aging transition. In particular, we present a control mechanism based on delayed…
We numerically investigate the effect of phase-amplitude coupling modulation on power spectra in semiconductor lasers subject to optical injection in a face to face configuration, when a non-negligible injection delay time is taken into…
We consider the effect of distributed delays in neural feedback systems. The avian optic tectum is reciprocally connected with the nucleus isthmi. Extracellular stimulation combined with intracellular recordings reveal a range of signal…
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…
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,…
We consider a general model for a network of oscillators with time delayed, circulant coupling. We use the theory of weakly coupled oscillators to reduce the system of delay differential equations to a phase model where the time delay…
We investigate the effects of heterogeneous delays in the coupling of two excitable neural systems. Depending upon the coupling strengths and the time delays in the mutual and self-coupling, the compound system exhibits different types of…
Many real-world examples of distributed oscillators involve not only time delays but also attractive (positive) and repulsive (negative) influences in their network interactions. Here, considering such examples, we generalize the Kuramoto…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
Many systems of physical and biological interest are characterized by assemblies of phase oscillators whose interaction is mediated by a diffusing chemical. The coupling effect results from the fact that the local concentration of the…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…