Related papers: Exponential decay for negative feedback loop with …
We study the decay properties of non-negative solutions to the one-dimensional defocusing damped wave equation in the Fujita subcritical case under a specific initial condition. Specifically, we assume that the initial data are positive,…
New methods are developed for the stabilization of a linear system with general time-varying distributed delays existing at the system's states, inputs and outputs. In contrast to most existing literature where the function of time-varying…
Two complementary analyses of a cyclic negative feedback system with delay are considered in this paper. The first analysis applies the work by Sontag, Angeli, Enciso and others regarding monotone control systems under negative feedback,…
This paper deals with some nonlinear problems which exponential and biexponential decays are involved in. A proof of the quasiconvexity of the error function in some of these problems of optimization is presented. This proof is restricted…
We analyze, both analytically and numerically, the time-dependence of the return probability in closed systems of interacting particles. Main attention is paid to the interplay between two regimes, one of which is characterized by the…
We consider small nonlinear perturbations of linear systems on a time scale with the phase space being finite or infinite-dimensional. For $\Delta$-differential operators, corresponding to linear dynamic systems we consider their…
We establish conditions guaranteeing that all eventually positive increasing solutions of a half-linear delay differential equation are regularly varying and derive precise asymptotic formulae for them. The results here presented are new…
We consider the problem of constructing Lyapunov functions for linear differential equations with delays. For such systems it is known that exponential stability implies the existence of a positive Lyapunov function which is quadratic on…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
The probability distribution of the proper delay times during scattering on a chaotic system is derived in the framework of the random matrix approach and the supersymmetry method. The result obtained is valid for an arbitrary number of…
We propose an analytical method for finding the time domain solution for the problem of electronic relaxation of a molecule in solution. The relaxation process is modeled by the decay of a diffusing probability distribution through an…
We develop a phase reduction method for reaction-diffusion systems with a discrete delay. On the basis of the recent developments in the phase reduction theory for infinite-dimensional systems, we introduce a bilinear form tailored to…
We propose an effective exponential model of delay discounting considering fluctuation in impulsivity. This model is seen to be dual to the two-parameter Tsallis model of delay discounting proposed by Takahashi in 2007. We demonstrate that…
In this paper we will study the asymptotic behaviour of the energy decay of a transmission plate equation with force and moment feedback. Precisly, we shall prove that the energy decay at least logarithmically over the time. The method…
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…
The time decay of fully discrete finite-volume approximations of porous-medium and fast-diffusion equations with Neumann or periodic boundary conditions is proved in the entropy sense. The algebraic or exponential decay rates are computed…
A mathematical model for the discrete nonlinear fragmentation (collision-induced breakage) equation with diffusion is studied. The existence of global weak solutions is established in arbitrary spatial dimensions without assuming a strictly…
This paper presents two new approaches for finding the homogenized coefficients of multiscale elliptic PDEs. Standard approaches for computing the homogenized coefficients suffer from the so-called resonance error, originating from a…
A new delay equation is introduced to describe the punctuated evolution of complex nonlinear systems. A detailed analytical and numerical investigation provides the classification of all possible types of solutions for the dynamics of a…
We consider an evolution equation whose time-diffusion is of fractional type and we provide decay estimates in time for the $L^s$-norm of the solutions in a bounded domain. The spatial operator that we take into account is very general and…