Related papers: Dissipative solitons for bistable delayed-feedback…

The elapsed-time model describes the behavior of interconnected neurons through the time since their last spike. It is an age-structured non-linear equation in which age corresponds to the elapsed time since the last discharge, and models…

The chaotic dynamics of directly modulated semiconductor lasers with delayed optoelectronic feedback is studied numerically. The effects of positive and negative delayed optoelectronic feedback in producing chaotic outputs from such lasers…

For the sake of saving time and costs the feedback control based on discrete-time observations is used to stabilize the switching diffusion systems. Response lags are required by most of physical systems and play a key role in the feedback…

Dark solitons carrying quantized phase information arouse great interest in different nonlinear systems. A dark soliton in 1D can be stabilized in microcavity polariton condensates as a confinement is imposed on it to prevent its decay.…

In the aerospace industry the trend for light-weight structures and the resulting complex dynamic behaviours currently challenge vibration engineers. In many cases, these light-weight structures deviate from linear behaviour, and complex…

We present a variety of dissipative solitons and breathing modes in a medium with localized gain and homogeneous linear dissipation. The system posses a number of unusual properties, like exponentially localized modes in both focusing and…

We consider the problem of the formation of soliton states from a modulationally unstable initial condition in the framework of the Schr\"odinger-Poisson (or Newton-Schr\"odinger) equation accounting for gravitational interactions. We…

We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.

This work models the propagation of an optical pulse in a 4-level atomic system in the electromagnetic induced transparency regime. By demonstrating that linear and nonlinear optical properties can be externally controlled and tailored by a…

We report results for solitons in models of waveguides with focusing or defocusing saturable nonlinearity and a parity-time(PT )-symmetric complex-valued external potential of the Scarf-II type. The model applies to the nonlinear wave…

Monotone systems comprise an important class of dynamical systems that are of interest both for their wide applicability and because of their interesting mathematical properties. It is known that under the property of quasimonotonicity…

Solitons are among the most distinguishing fundamental excitations in a wide range of non-linear systems such as water in narrow channels, high speed optical communication, molecular biology and astrophysics. Stabilized by a balance between…

We reveal the existence of slowly-decaying dark solitons in the radiation build-up dynamics of bright pulses in all-normal dispersion mode-locked fiber lasers, numerically modeled in the framework of a generalized nonlinear Schr\"odinger…

Understanding how time delays impact the stability of a delay differential equation is important for modeling many natural and technological systems that experience time delays. Here we introduce a new stability criterion for…

We consider nonlinear effects in scattering of light by a periodic structure supporting optical bound states in the continuum. In the spectral vicinity of the bound states the scattered electromagnetic field is resonantly enhanced…

We show that the nonlinear polarization dynamics of a vertical-cavity surface-emitting laser placed into an external cavity leads to the formation of temporal vectorial dissipative solitons. These solitons arise as cycles in the…

Much recent progress has been achieved for stabilization of linear and nonlinear systems with input delays that are long and dependent on either time or the plant state---provided the dependence is known. In this paper we consider the delay…

We study the formation of bright solitons in a Bose-Einstein condensate of $^7$Li atoms induced by a sudden change in the sign of the scattering length from positive to negative, as reported in a recent experiment (Nature {\bf 417}, 150…

This paper studies integral input-to-state stability (iISS) of nonlinear impulsive systems with time-delay in both the continuous dynamics and the impulses. Several iISS results are established by using the method of Lyapunov-Krasovskii…

Partial differential equations with discrete (concentrated) state-dependent delays in the space of continuous functions are investigated. In general, the corresponding initial value problem is not well posed, so we find an additional…