Related papers: Differential equations with discrete state-depende…
We study, by means of a topological approach, the forced oscillations of second order functional retarded differential equations subject to periodic perturbations. We consider a delay-type functional dependence involving a gamma probability…
This is the first of a two-part paper which determines necessary and sufficient conditions on the asymptotic behaviour of forcing functions so that the solutions of additively pertubed linear differential equations obey certain growth or…
This article aims to investigate sufficient conditions for the stability of stochastic differential equations with a random structure, particularly in contexts involving the presence of concentration points. The proof of asymptotic…
For a large family of nonautonomous scalar-delayed differential equations used in population dynamics, some criteria for permanence are given, as well as explicit upper and lower bounds for the asymptotic behavior of solutions. The method…
We develop categorical foundations of discrete dynamical systems, aimed at understanding how the structure of the system affects its dynamics. The key technical innovation is the notion of a cycle set, which provides a formal language in…
We study stochastic delay differential equations (SDDE) where the coefficients depend on the moving averages of the state process. As a first contribution, we provide sufficient conditions under which a linear path functional of the…
It is known that input-output approaches based on scaled small-gain theorems with constant $D$-scalings and integral linear constraints are non-conservative for the analysis of some classes of linear positive systems interconnected with…
We examine an infinite, linear system of ordinary differential equations that models the evolution of fragmenting clusters, where each cluster is assumed to be composed of identical units. In contrast to previous investigations into such…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
This paper examines a system of partial differential equations describing dislocation dynamics in a crystalline solid. In particular we consider dynamics linearized about a state of zero stress and use linear semigroup theory to establish…
We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or distributed delays (forward or backward). We show that,…
We study the asymptotic behavior of solutions of discrete nonlinear Schr\"odinger-type (DNLS) equations. For a conservative system, we consider the global in time solvability and the question of existence of standing wave solutions.…
We study the well-posedness and asymptotic behaviour of selected PDE-PDE and PDE-ODE systems on one-dimensional spatial domains, namely a boundary coupled wave-heat system and a wave equation with a dynamic boundary condition. We prove…
We present a condition for delay-independent stability of a class of nonlinear positive systems. This result applies to systems that are not necessarily monotone and extends recent work on cooperative nonlinear systems.
For a mixed stochastic differential equation involving standard Brownian motion and an almost surely H\"older continuous process $Z$ with H\"older exponent $\gamma>1/2$, we establish a new result on its unique solvability. We also establish…
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…
Time delays are a common perturbation in systems with many states, such as networked, distributed, or decentralized systems. Current methods analyzing the stability of large systems with time delay typically produce very conservative…
The solvability and stability analysis of linear time invariant systems of delay differential-algebraic equations (DDAEs) is analyzed. The behavior approach is applied to DDAEs in order to establish characterizations of their solvability in…
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…
This paper extends the core results of discrete time infinite horizon dynamic programming to the case of state-dependent discounting. We obtain a condition on the discount factor process under which all of the standard optimality results…