Related papers: Phase reduction theory for hybrid nonlinear oscill…
Multirhythmicity, a form of multistability, in an oscillator is an intriguing phenomenon found across many branches of science. From an application point of view, while the multirhythmicity is sometimes desirable as it presents us with many…
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…
Given the high dimensionality and underlying complexity of many oscillatory dynamical systems, phase reduction is often an imperative first step in control applications where oscillation timing and entrainment are of interest.…
We explore the interplay of network structure, topology, and dynamic interactions between nodes using the paradigm of distributed synchronization in a network of coupled oscillators. As the network evolves to a global steady state,…
After decades of study, there are only two known mechanisms to induce global synchronization in a population of oscillators: deterministic coupling and common forcing. The inclusion of independent random forcing in these models typically…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
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 a driven oscillator loses phase-locking to a master oscillator via a Hopf bifurcation, it enters a bounded-phase regime in which its average frequency is still equal to the master frequency, but its phase displays temporal…
Coupled oscillators have been used to study synchronization in a wide range of social, biological, and physical systems, including pedestrian-induced bridge resonances, coordinated lighting up of firefly swarms, and enhanced output peak…
This paper investigates the stability properties and performance of super-twisting sliding-mode control loops subject to periodic perturbations. Although there exist conditions on the control gains that guarantee finite-time stability of…
Shared upstream dynamical processes are frequently the source of common inputs in various physical and biological systems. However, due to finite signal transmission speeds and differences in the distance to the source, time shifts between…
This study explores a method to characterize temporal structure of intermittent phase locking in oscillatory systems. When an oscillatory system is in a weakly synchronized regime away from a synchronization threshold, it spends most of the…
We study collective behavior of locally coupled limit-cycle oscillators with random intrinsic frequencies, spatially extended over $d$-dimensional hypercubic lattices. Phase synchronization as well as frequency entrainment are explored…
This study investigates the synchronization dynamics of coupled-oscillator systems in which some of the oscillators are damaged and lose their autonomous oscillations. The damaged elements are modeled using damped oscillators; thus, the…
We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…
The notion of phase synchronization in time-delay systems, exhibiting highly non-phase-coherent attractors, has not been realized yet even though it has been well studied in chaotic dynamical systems without delay. We report the…
In the present work, we consider nonlinear control systems for which there exist structural obstacles to the design of classical continuous backstepping feedback laws. We conceive feedback laws such that the origin of the closed-loop system…
Oscillators - dynamical systems with stable periodic orbits - arise in many systems of physical, technological, and biological interest. The standard phase reduction, a model reduction technique based on isochrons, can be unsuitable for…
We study control of synchronization in weakly coupled oscillator networks by using a phase reduction approach. Starting from a general class of limit cycle oscillators we derive a phase model, which shows that delayed feedback control…
In this paper we use the parameterization method to provide a complete description of the dynamics of an $n$-dimensional oscillator beyond the classical phase reduction. The parameterization method allows, via efficient algorithms, to…