Related papers: Singularly perturbed phase response curves
We provide a justification with rigorous error estimates showing that the leading term in weakly nonlinear geometric optics expansions of highly oscillatory reflecting pulses is close to the uniquely determined exact solution for small…
Phase response curve is an important tool in studies of stable self-sustained oscillations; it describes a phase shift under action of an external perturbation. We consider multistable oscillators with several stable limit cycles. Under a…
Exact coherent states in the Calogero-Sutherland models (of time-dependent parameters) which describe identical harmonic oscillators interacting through inverse-square potentials are constructed, in terms of the classical solutions of a…
We study a third-order nonlinear ordinary differential equation whose solutions, under certain specific conditions, are individual pulses. These correspond to homoclinic orbits in the phase space of the equation and we study the possible…
For a system of globally pulse-coupled phase-oscillators, we derive conditions for stability of the completely synchronous state and all possible two-cluster states and explain how the different states are naturally connected via…
We present a novel method for high-order phase reduction in networks of weakly coupled oscillators and, more generally, perturbations of reducible normally hyperbolic (quasi-)periodic tori. Our method works by computing an asymptotic…
We formulate a renormalization group approach to a general nonlinear oscillator problem. The approach is based on the exact group law obeyed by solutions of the corresponding ordinary differential equation. We consider both the autonomous…
We analyze limit cycle oscillators under perturbation constructed as a product of two signals, namely, an envelope with a period close to natural period of an oscillator and a high-frequency carrier signal. A theory for obtaining an…
The onset of collective behavior in a population of globally coupled oscillators with randomly distributed frequencies is studied for phase dynamical models with arbitrary coupling; the effect of a stochastic temporal variation in the…
In this paper, we present output feedback boundary stabilization for a class of semilinear parabolic PDEs with a boundary measurement and an actuation located at the same place. The method uses backstepping transformations, where the state…
We consider a continuum of phase oscillators on the circle interacting through an impulsive instantaneous coupling. In contrast with previous studies on related pulse-coupled models, the stability results obtained in the continuum limit are…
This work is motivated by a desire to understand transitions between stable equilibria observed in Stommel's 1961 thermohaline circulation model. We adapt the model, including a forcing parameter as a dynamic slow variable. The resulting…
In this article, we study some anisotropic singular perturbations for a class of linear elliptic problems. A uniform estimates for conforming $Q_1$ finite element method are derived, and some other results of convergence and regularity for…
We discuss applications of time-delayed feedback control to delay-coupled neural systems and lasers, in the framework of the FitzHugh-Nagumo neuron model and the Lang-Kobayashi laser model, respectively. In the context of neural systems, we…
A wave front and a wave back that spontaneously connect two hyperbolic equilibria, known as a heteroclinic wave loop, give rise to periodic waves with arbitrarily large spatial periods through the heteroclinic bifurcation. The nonlinear…
Linearization around unstable travelling waves in excitable systems can be used to approximate strength-extent curves in the problem of initiation of excitation waves for a family of spatially confined perturbations to the rest state. This…
We consider a network of identical pulse-coupled oscillators with delay and all-to-all coupling. We demonstrate that the discontinuous nature of the dynamics induces the appearance of isochronous regions---subsets of the phase space filled…
The activity of collections of synchronizing neurons can be represented by weakly coupled nonlinear phase oscillators satisfying Kuramoto's equations. In this article, we build such neural-oscillator models, partly based on…
Synchronization phenomena, frequency shift and phase noise are often limiting key factors in the performances of oscillators. The perturbation projection method allows to characterize how the oscillator's output is modified by these…
Large-scale simulations of the wave equation in electromagnetism, seismology, and acoustics, can be solved efficiently by finite difference methods. The accuracy of these numerical solutions usually depends on the minimization of…