Related papers: A delay differential eqution NOLM-NALM mode-locked…
We describe a method to model nonlinear dynamical systems using periodic solutions of delay-differential equations. We show that any finite-time trajectory of a nonlinear dynamical system can be loaded approximately into the initial…
We report the first experimental observation of discrete time-crystal phases and crystallites in an actively mode-locked semiconductor laser. By tuning either the bias current or the modulation frequency, the system undergoes a spontaneous…
Coherent mode-locking (CML) uses self-induced transparency (SIT) soliton formation to achieve, in contrast to conventional schemes based on absorption saturation, the pulse durations below the limit allowed by the gain line width. Despite…
Moving the fiber laser emission to the region below one micron may provide a cheaper, more compact and robust alternatives to the existing solid state lasers. Here, for the first time we report a neodymium mode-locked fiber laser emitting…
We study delay-independent stability in nonlinear models with a distributed delay which have a positive equilibrium. Such models frequently occur in population dynamics and other applications. In particular, we construct a relevant…
We demonstrate for a nonlinear photonic system that two highly asymmetric feedback delays can induce a variety of emergent patterns which are highly robust during the system's global evolution. Explicitly, two-dimensional chimeras and…
Passively mode-locked semiconductor disk lasers have received tremendous attention from both science and industry. Their relatively inexpensive production combined with excellent pulse performance and great emission wavelength flexibility…
We study the stability of general $n$-dimensional nonautonomous linear differential equations with infinite delays. Delay independent criteria, as well as criteria depending on the size of some finite delays are established. In the first…
Dissipative nonlinear wave dynamics have been investigated extensively in mode-locked lasers with single transverse-mode, whereas there are few studies related to three-dimensional nonlinear dynamics within lasers. Recently, spatiotemporal…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
Mode-locking is predicted in a nanolaser cavity forming an effective photonic harmonic potential. The cavity is substantially more compact than a Fabry-Perot resonator with comparable pulsing period, which is here controlled by the…
A study of the non linear modes of a two degree of freedom mechanical system with bilateral elastic stop is considered. The issue related to the non-smoothness of the impact force is handled through a regularization technique. In order to…
This paper is devoted to the study of the stability of limit cycles of a nonlinear delay differential equation with a distributed delay. The equation arises from a model of population dynamics describing the evolution of a pluripotent stem…
We report experimental studies of the influence of symmetric dual-loop optical feedback on the RF linewidth and timing jitter of self-mode-locked two-section quantum dash lasers emitting at 1550 nm. Various feedback schemes were…
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 investigate the dynamics of a delay differential coupled Duffing-Van der Pol oscillator equation. Using the Lindstedt's method, we derive the in-phase mode solutions and then obtain the slow flow equations governing the stability of the…
Time lags occur in a vast range of real-world dynamical systems due to finite reaction times or propagation speeds. Here we derive an analytical approach to determine the asymptotic stability of synchronous states in networks of coupled…
A self-consistent integral equation is formulated and solved iteratively which determines the steady-state lasing modes of open multi-mode lasers. These modes are naturally decomposed in terms of frequency dependent biorthogonal modes of a…
Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…
Linear scalar differential equations with distributed delays appear in the study of the local stability of nonlinear differential equations with feedback, which are common in biology and physics. Negative feedback loops tend to promote…