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Kink oscillations in coronal loops have been extensively studied for their potential contributions to coronal heating and their role in plasma diagnostics through coronal seismology. A key focus is the strong damping of large-amplitude kink…
Mounting evidence shows that oscillatory activity is widespread in cell signaling. Here we review some of this recent evidence, focusing on both the molecular mechanisms that potentially underlie such dynamical behavior, and the potential…
Pulse-coupled systems such as spiking neural networks exhibit nontrivial invariant sets in the form of attracting yet unstable saddle periodic orbits where units are synchronized into groups. Heteroclinic connections between such orbits may…
Fluid dynamics induced by periodically forced flow around a cylinder is analyzed computationally for the case when the forcing frequency is much lower than the von K{\'a}rm{\'a}n vortex shedding frequency corresponding to the constant flow…
The bifurcation structure of coupled periodically driven double-well Duffing oscillators is investigated as a function of the strength of the driving force $f$ and its frequency $\Omega$. We first examine the stability of the steady state…
We present our study on the emergent states of two interacting nonlinear systems with differing dynamical time scales. We find that the inability of the interacting systems to fall in step leads to difference in phase as well as change in…
This paper is concerned with the analysis of a class of impacting systems of relevance in applications: cam-follower systems. We show that these systems, which can be modelled as discontinuously forced impact oscillators, can exhibit…
The spontaneous generation of electrical activity underpins a number of essential physiological processes, and is observed even in tissues where specialized pacemaker cells have not been identified. The emergence of periodic oscillations in…
The phase oscillator model with global coupling is extended to the case of finite-range nonlocal coupling. Under suitable conditions, peculiar patterns emerge in which a quasi-continuous array of identical oscillators separates sharply into…
For a class of coupled limit cycle oscillators, we give a condition on a linear coupling operator that is necessary and sufficient for exponential stability of the synchronous solution. We show that with certain modifications our method of…
We demonstrate the emergence of self-organized structures in the course of the relaxation of an initially excited, dissipative and finite chain of interacting particles in a periodic potential towards its many particle equilibrium…
We report the occurrence of a self-emerging frequency chimera state in spatially extended systems of coupled oscillators, where the coherence and incoherence are defined with respect to the emergent frequency of the oscillations. This is…
We investigated the locking behaviors of coupled limit-cycle oscillators with phase and amplitude dynamics. We focused on how the dynamics are affected by inhomogeneous coupling strength and by angular and radial shifts in the coupling…
When an oscillator switches abruptly between different frequencies, there is some ambiguity in deciding how the system should be modelled at the switch. Here we describe two seemingly natural models of a switch in a simple…
Uncovering and understanding universal dynamics in matter far from equilibrium remains a key challenge. In this work, we identify a so far unrecognized form of universal behavior that emerges after a sudden symmetry-breaking quench at…
We obtain analytical results for the time evolution of local observables in systems undergoing quantum quenches in $d$ spatial dimensions. For homogeneous systems we show that oscillations undamped in time occur when the state produced by…
Finding conditions that support synchronization is a fertile and active area of research with applications across multiple disciplines. Here we present and analyze a scheme for synchronizing chaotic dynamical systems by transiently…
Quenching of limit cycle oscillations (LCO), either through mutual coupling or external forcing, has attracted wide attention in several fields of science and engineering. However, the simultaneous utilization of these coupling schemes in…
We investigate the quantum dynamics of many-body systems subject to local, i.e. restricted to a limited space region, time-dependent perturbations. If the perturbation drives the system across a quantum transition, an off-equilibrium…
We introduce a method to identify phase equations that include $N$-body interactions for general coupled oscillators valid far beyond the weak coupling approximation. This strategy is an extension of the theory from [Park and Wilson, SIADS…