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The synchronization analysis of limit-cycle oscillators is prevalent in many fields, including physics, chemistry, and life sciences. It relies on the phase calculation that utilizes measurements. However, the synchronization of…
Oscillations and noise are ubiquitous in physical and biological systems. When oscillations arise from a deterministic limit cycle, entrainment and synchronization may be analyzed in terms of the asymptotic phase function. In the presence…
The phase reduction technique is essential for studying rhythmic phenomena across various scientific fields. It allows the complex dynamics of high-dimensional oscillatory systems to be expressed by a single phase variable. This paper…
We study the effects of a probabilistic refractory period in the collective behavior of coupled discrete-time excitable cells (SIRS-like cellular automata). Using mean-field analysis and simulations, we show that a synchronized phase with…
Stochastic resonance is a general phenomenon usually observed in one-dimensional, amplitude modulated, bistable systems.We show experimentally the emergence of phase stochastic resonance in the bidimensional response of a forced…
In the data analysis of oscillatory systems, methods based on phase reconstruction are widely used to characterize phase-locking properties and inferring the phase dynamics. The main component in these studies is an extraction of the phase…
Many systems in physics, chemistry and biology exhibit oscillations with a pronounced random component. Such stochastic oscillations can emerge via different mechanisms, for example linear dynamics of a stable focus with fluctuations,…
Partial synchronous states appear between full synchrony and asynchrony and exhibit many interesting properties. Most frequently, these states are studied within the framework of phase approximation. The latter is used ubiquitously to…
Over the last half century the liquid-gas phase transition and the magnetization phase transition have come to be well understood. After an order parameter, $r$, is defined, it can be derived how $r=0$ for $T>T_c$ and how $r \propto (T_c -…
The combined influence of oscillatory excitations and multiplicative stochastic perturbations of white noise type on isochronous systems in the plane is investigated. It is assumed that the intensity of perturbations decays with time and…
An oscillator is called isochronous if all motions have a common period. When the system is forced by a time-dependent perturbation with the same period the dynamics may change and the phenomenon of resonance can appear. In this context,…
We investigate both continuous (second-order) and discontinuous (first-order) transitions to macroscopic synchronization within a single class of discrete, stochastic (globally) phase-coupled oscillators. We provide analytical and numerical…
Stochastic resets have lately emerged as a mechanism able to generate finite equilibrium mean square displacement (MSD) when they are applied to diffusive motion. Furthermore, walkers with an infinite mean first arrival time (MFAT) to a…
The coupled Stuart-Landau equation serves as a fundamental model for exploring synchronization and emergent behavior in complex dynamical systems. However, understanding its dynamics from a comprehensive nonlinear perspective remains…
Definition of the phase of oscillations is straightforward for deterministic periodic processes but nontrivial for stochastic ones. Recently, Thomas and Lindner in [Phys. Rev. Lett., v. 113, 254101 (2014)] suggested to use the argument of…
Phase reduction is an important tool for studying coupled and driven oscillators. The question of how to generalize phase reduction to stochastic oscillators remains actively debated. In this work, we propose a method to derive a…
Phase reduction is a well-established technique used to analyze the timing of oscillations in response to weak external inputs. In the preceding decades, a wide variety of results have been obtained for weakly perturbed oscillators that…
In a previous work by the first author with J. Turi (AMO, 08), a stochastic variational inequality has been introduced to model an elasto-plastic oscillator with noise. A major advantage of the stochastic variational inequality is to…
Stochastic differential equations and the associated partial differential equations are the cornerstone formalism in stochastic control problems. The universality of bilinear stochastic systems can be found in autonomous systems, non-linear…
Isoscalar and isovector monopole oscillations that correspond to giant resonances in spherical nuclei are described in the framework of time-dependent relativistic mean-field theory. Time-dependent and self-consistent calculations that…