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We theoretically investigate the possibility of observing resonant activation in the hopping dynamics of two-mode semiconductor lasers. We present a series of simulations of a rate-equations model under random and periodic modulation of the…
A variant of the complex Ginzburg-Landau equation is used to investigate the frequency locking phenomena in spatially extended systems. With appropriate parameter values, a variety of frequency-locked patterns including flats, $\pi$ fronts,…
We present a detailed study of the effect of time delay on the collective dynamics of coupled limit cycle oscillators at Hopf bifurcation. For a simple model consisting of just two oscillators with a time delayed coupling, the bifurcation…
Interaction via pulses is common in many natural systems, especially neuronal. In this article we study one of the simplest possible systems with pulse interaction: a phase oscillator with delayed pulsatile feedback. When the oscillator…
Robust heteroclinic cycles are known to change stability in resonance bifurcations, which occur when an algebraic condition on the eigenvalues of the system is satisfied and which typically result in the creation or destruction of a…
The correlation function of radiation from a high-quality semiconductor microcavity at the resonant laser excitation demonstrates oscillations with surprisingly long-period and damping times of a nanosecond range. It was shown that the…
We study scalar delay equations $$\dot{x} (t) = \lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2))$$ with odd nonlinearity $f$, real nonzero parameters $\lambda, \, b$, and two positive time delays $1,\ p/2$. We assume supercritical…
We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…
The behavior of delta-doped wide quantum well heterostructures in the presence of intense far-infrared radiation is studied using semiconductor Bloch equations. A quantum well is designed where one can either obtain a strong subharmonic…
We present the first experimental confirmation of the so-called "self-phaselocked delay interferometry". This laser frequency stabilization technique consists basically in comparing the prompt laser signal with a delayed version of itself…
We investigate bifurcation phenomena between slow and fast convergences of synchronization errors arising in the proposed synchronization system consisting of two identical nonlinear dynamical systems linked by a common noisy input only.…
We study the primary bifurcations of a two-dimensional Kolmogorov flow in a channel subject to boundary conditions chosen to mimic a parallel flow, i.e. periodic and free-slip boundary conditions in the streamwise and spanwise directions,…
We present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one…
Microresonator frequency combs, essential for future integrated optical systems, rely on dissipative Kerr solitons generated in a single microresonator to achieve coherent frequency comb generation. Recent advances in the nanofabrication of…
We study the existence and stability of phaselocked patterns and amplitude death states in a closed chain of delay coupled identical limit cycle oscillators that are near a supercritical Hopf bifurcation. The coupling is limited to nearest…
We demonstrate a method that enables accurate timing jitter spectral density characterization of free-running mode-locked laser oscillators over more than 10-decade of Fourier frequency from mHz to tens MHz range. The method is based on…
This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing…
We present a novel approach for the analysis of passively mode-locked semiconductor lasers that allows for efficient parameter sweeps and time jitter analysis. It permits accessing the ultra-low repetition rate regime where pulses become…
Motivated by recent experimental observations concerning the polarization dynamics in an excitable microlaser with saturable absorber coupled to an external feedback mirror reported in [Ruschel et al. (2025) Opt. Lett. 50 (8) 2618], we…
The spectrum of the generator (Kolmogorov operator) of a diffusion process, referred to as the Ruelle-Pollicott (RP) spectrum, provides a detailed characterization of correlation functions and power spectra of stochastic systems via…