Related papers: Multi-pulse phase resetting curve
We report results on a model of two coupled oscillators that undergo periodic parametric modulations with a phase difference $\theta$. Being to a large extent analytically solvable, the model reveals a rich $\theta$ dependence of the…
The problem of the effect of two-frequency quasi-periodic perturbations on systems close to arbitrary nonlinear two-dimensional Hamiltonian ones is studied in the case when the corresponding perturbed autonomous systems have a double limit…
The influence of oscillatory perturbations on autonomous strongly nonlinear systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time, and their frequency increases according to a power law.…
The phase reduction method for a limit cycle oscillator subjected to a strong amplitude-modulated high-frequency force is developed. An equation for the phase dynamics is derived by introducing a new, effective phase response curve. We show…
We report on an extension of the concept of nonlinear self-repolarization process by means of two different architectures based on dual-Omnipolarizers. More specifically, we compare the performance in terms of polarization attraction…
Pulse-coupled threshold units serve as paradigmatic models for a wide range of complex systems. When the state variable of a unit crosses a threshold, the unit sends a pulse that is received by other units, thereby mediating the…
The "Phase Response Curve" (PRC) is a common tool used to analyze phase resetting in the natural sciences. We make the observation that the PRC with respect to a coordinate $y\in\mathbb{R}$ actually depends on the full choice of coordinates…
The effects of spike timing precision and dynamical behavior on error correction in spiking neurons were investigated. Stationary discharges -- phase locked, quasiperiodic, or chaotic -- were induced in a simulated neuron by presenting…
We report the synchronization behavior in a one-dimensional chain of identical limit cycle oscillators coupled to a mass-spring load via a force relation. We consider the effect of periodic parametric modulation on the final synchronization…
The Duffing oscillator is a nonlinear extension of the ubiquitous harmonic oscillator and as such plays an outstanding role in science and technology. Experimentally, the system parameters are determined by a measurement of its response to…
We investigate the combined effect of rectification and nonlinear dynamics on the behavior of several simple nonlinear circuits. We consider the classic Resistor-Inductor-Diode (RLD) circuit driven by a low frequency source when an…
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…
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…
Rhythmic behaviors in neural systems often combine features of limit cycle dynamics (stability and periodicity) with features of near heteroclinic or near homoclinic cycle dynamics (extended dwell times in localized regions of phase space).…
The circadian clocks keeping time of day in many living organisms rely on self-sustained biochemical oscillations which can be entrained by external cues, such as light, to the 24-hour cycle induced by Earth rotation. However, environmental…
We show that a large class of pulse coupled oscillators converge with high probability from random initial conditions on a large class of graphs with time delays. Our analysis combines previous local convergence results, probabilistic…
A new type of perturbative expansion is built in order to give a rigorous derivation and to clarify the range of validity of some commonly used model equations. This model describes the evolution of the modulation of two short and localized…
Radio pulsar polarization exhibits a number of complex phenomena that are classified into the realm of `beyond the rotating vector model' (RVM). It is shown that these effects can be understood in geometrical terms, as a result of coherent…
We investigate the dynamical motion of particles on a two-dimensional symmetric periodic substrate in the presence of both a dc drive along a symmetry direction of the periodic substrate and an additional circular ac drive. For large enough…
A system of two coupled semiconductor-based resonators is studied when lasing around an exceptional point. We show that the presence of nonlinear saturation effects can have important ramifications on the transition behavior of this system.…