Related papers: A Discrete-Time, Time-Delayed Lur'e Model with Bia…

Time delays due to signal latency, computational complexity, and sensor-denied environments, pose a critical challenge in both engineered and biological control systems. In this work, we investigate biologically inspired strategies to…

Frequency domain analysis of linear time-invariant (LTI) systems in feedback with static nonlinearities is a classical and fruitful topic of nonlinear systems theory. We generalize this approach beyond equilibrium stability analysis with…

Autonomous oscillators, such as clocks and lasers, produce periodic signals \emph{without} any external frequency reference. In order to sustain stable periodic motions, there needs to be external energy supply as well as nonlinearity built…

Gene expression time delays, modelling the complex biological processes of gene transcription and translation, have been shown to play an important role in cellular dynamics. Time delays, motivated by the gene expression process, can also…

Self-organized network dynamics prevails for systems across physics, biology and engineering. How external signals generate distributed responses in networked systems fundamentally underlies their function, yet is far from fully understood.…

We investigate a control of the motion of localized structures of light by means of delay feedback in the transverse section of a broad area nonlinear optical system. The delayed feedback is found to induce a spontaneous motion of a…

In this article a generalized mathematical model describing the interactions between malignant tumour and immune system with discrete time delay incorporated into the system is considered. Time delay represents the time required to generate…

We analyze the stability properties of Lur'e systems with piecewise continuous nonlinearities by exploiting the notion of set-valued Lie derivative for Lur'e-Postnikov Lyapunov functions. We first extend an existing result of the literature…

For most stochastic dynamical systems, variables which are tightly regulated tend to respond slowly to external changes. This idea is often discussed for applicable systems, within a linear response regime, through the Fluctuation…

We report on collective excitable events in a highly-diluted random network of non-excitable nodes. Excitability arises thanks to a self-sustained local adaptation mechanism that drives the system on a slow time-scale across a hysteretic…

We investigate the oscillatory dynamics and bifurcation structure of a reaction-diffusion system with bistable nonlinearity and mass conservation, which was proposed by [Otsuji et al, PLoS Comp. Biol. 3 (2007), e108]. The system is a useful…

We investigated the phenomena of self-stimulation of incoherent emission from an undulator installed in the linear accelerator or quasi-isochronous storage ring. We discuss possible applications of these phenomena for the beam physics also.

Retarded stochastic differential equations (SDEs) constitute a large collection of systems arising in various real-life applications. Most of the existing results make crucial use of dissipative conditions. Dealing with "pure delay" systems…

Oscillatory chemical reactions often serve as a timing clock of cellular processes in living cells. The temporal dynamics of protein concentration levels is thus of great interest in biology. Here we propose a theoretical framework to…

We demonstrate experimental exploration of the attractor diagram of an optomechanical system where the optical forces compensate for the mechanical losses. In this case stable self-induced oscillations occur but only for specific mirror…

The neural ordinary differential equation (ODE) framework has emerged as a powerful tool for developing accelerated surrogate models of complex physical systems governed by partial differential equations (PDEs). A popular approach for PDE…

Reed instruments are modeled as self-sustained oscillators driven by the pressure inside the mouth of the musician. A set of nonlinear equations connects the control parameters (mouth pressure, lip force) to the system output, hereby…

We consider a nonlinear model for electrical conduction in biological tissues. The nonlinearity appears in the interface condition prescribed on the cell membrane. The purpose of this paper is proving asymptotic convergence for large times…

A system of ODE's is used to approximate the dynamics of two delayed coupled FitzHugh-Nagumo excitable units, and study the relevant bifurcations. It is shown that the Bautin bifurcation acts as the organizing center for the dynamics of…

Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying…