Related papers: Practicalities of State-Dependent and Threshold De…
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…
Linear stability of synchronized states in networks of delay-coupled oscillators depends on the type of interaction, the network and oscillator properties. For inert oscillator response, found ubiquitously from biology to engineering,…
Systems with time delay play an important role in modeling of many physical and biological processes. In this paper we describe generic properties of systems with time delay, which are related to the appearance and stability of periodic…
Classically, solution theories for state-dependent delay equations are developed in spaces of continuous or continuously differentiable functions. The former can be technically challenging to apply in as much as suitably Lipschitz…
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…
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…
Mathematical modeling based on time-delay differential equations is an important tool to study the role of delay in biological systems and to evaluate its impact on the asymptotic behavior of their dynamics. Delays are indeed found in many…
The paper discusses linear fractional representations of parameter-dependent nonlinear systems with dynamics defined by real rational nonlinearities and a finite set of point delays. The global asymptotic stability is investigated via…
In this paper we study stochastic control problems with delayed information, that is, the control at time $t$ can depend only on the information observed before time $t-H$ for some delay parameter $H$. Such delay occurs frequently in…
The task of state estimation in active distribution systems faces a major challenge due to the integration of different measurements with multiple reporting rates. As a result, distribution systems are essentially unobservable in real time,…
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…
We investigate state dependent delay differential equations with distributed memory, combining discrete state dependent delays and a convolution type memory operator. Under Lipschitz type assumptions on the delay, kernel, and nonlinear…
In this work, we shall consider the existence and uniqueness of stationary solutions to stochastic partial functional differential equations with additive noise in which a neutral type of delay is explicitly presented. We are especially…
We study the impact of competing time delays in coupled stochastic synchronization and coordination problems. We consider two types of delays: transmission delays between interacting elements and processing, cognitive, or execution delays…
Differential equations (DEs) are commonly used to describe dynamic systems evolving in one (ordinary differential equations or ODEs) or in more than one dimensions (partial differential equations or PDEs). In real data applications the…
Parabolic differential equations with discrete state-dependent delay are studied. The approach, based on an additional condition on the delay function introduced in [A.V. Rezounenko, Differential equations with discrete state-dependent…
This paper deals a continuous-time state-dependent jump linear system, a particular kind of stochastic switching system. In particular, we consider a situation when the transition rate of the random jump process depends on the state…
In the present article, we discuss some aspects of the local stability analysis for a class of abstract functional differential equations. This is done under smoothness assumptions which are often satisfied in the presence of a…
In realistic pursuit-evasion scenarios, abrupt target maneuvers generate unavoidable periods of elevated uncertainty that result in estimation delays. Such delays can degrade interception performance to the point of causing a miss. Existing…
We explore probability modelling of discretization uncertainty for system states defined implicitly by ordinary or partial differential equations. Accounting for this uncertainty can avoid posterior under-coverage when likelihoods are…