Related papers: Spectral dominance of complex roots for single-del…
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…
This paper presents two new constructions related to singular solutions of polynomial systems. The first is a new deflation method for an isolated singular root. This construc-tion uses a single linear differential form defined from the…
While the asymptotic stability of positive linear systems in the presence of bounded time delays has been thoroughly investigated, the theory for nonlinear positive systems is considerably less well-developed. This paper presents a set of…
In this paper, we investigate a system composed of two degenerate wave equations which are connected at one point. By introducing some inequalities on the weighted spaces and employing the frequency domain method, we prove that the system…
A characteristic matrix function captures the spectral information of a bounded linear operator in a matrix-valued function. In this article, we consider a delay differential equation with one discrete time delay and assume this equation is…
Active agents with time-delayed interactions arise naturally in various real-world systems, such as biological systems, transportation networks and robotic swarms. Such systems are typically modeled as Delay Differential Equations (DDEs)…
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…
Research of delayed neural networks with variable self-inhibitions, inter-connection weights, and inputs is an important issue. %In the real world, self-inhibitions, %inter-connection weights, and inputs should vary through time. In In this…
In this paper, we obtain sufficient conditions for the permanence of a family of nonautonomous systems of delay differential equations. This family includes structured models from mathematical biology, with either discrete or distributed…
We analyze the density of roots of random polynomials where each complex coefficient is constructed of a random modulus and a fixed, deterministic phase. The density of roots is shown to possess a singular component only in the case for…
The location of roots of the characteristic equation of a linear delay differential equation (DDE) determines the stability of the linear DDE. However, by its transcendency, there is no general criterion on the contained parameters for the…
Two-particle scattering amplitudes for integrable relativistic quantum field theory in 1+1 dimensions can normally have at most singularities of poles and zeros along the imaginary axis in the complex rapidity plane. It has been supposed…
We investigate the plane dynamical system given by the secant map applied to a polynomial $p$ having at least one multiple root of multiplicity $d>1$. We prove that the local dynamics around the fixed points associated to the roots of $p$…
Despite its nonconvexity, policy optimization for the Linear Quadratic Regulator (LQR) admits a favorable structural property known as gradient dominance, which facilitates linear convergence of policy gradient methods to the globally…
A general nonautonomous Nicholson equation with multiple pairs of delays in {\it mixed monotone} nonlinear terms is studied. Sufficient conditions for permanence are given, with explicit lower and upper uniform bounds for all positive…
We study here a model of globally coupled units with adaptive interaction weights which has a delay in the updating rule. Simulations show that the model with such delayed synaptic change exhibits dynamical self-organization of network…
In our manuscript, we develop a new approach for stability analysis of one-dimensional wave equation with time delay. The major contribution of our work is to develop a new method for spectral analysis. We derive sufficient and necessary…
We study discrete time linear constrained switching systems with additive disturbances, in which the switching may be on the system matrices, the disturbance sets, the state constraint sets or a combination of the above. In our general…
Oscillatory dynamics are common features of complex networks, often playing essential roles in regulating function. Across scales from gene regulatory networks to ecosystems, delayed feedback mechanisms are key drivers of system-scale…
Multidimensional systems coupled via complex networks are widespread in nature and thus frequently invoked for a large plethora of interesting applications. From ecology to physics, individual entities in mutual interactions are grouped in…