Related papers: Permanence for nonautonomous differential systems …
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…
Delay differential equations are used as a model when the effect of past states has to be taken into account. In this work we consider delay models of chemical reaction networks with mass action kinetics. We obtain a sufficient condition…
A class of discrete-time nonlinear positive time-delay switched systems with sector-type nonlinearities is studied. Sufficient conditions for the existence of common and switched diagonal Lyapunov--Krasovskii functionals for this system…
This paper studies a class of random nonlinear systems with time-varying delay, in which the $r$-order moment ($r\geq1$) of the random disturbance is finite. Firstly, some general conditions are proposed to guarantee the existence and…
Time-invariant finite-dimensional systems, under reasonable continuity assumptions, exhibit the property that if solutions exist for all future times, the set of vectors reachable from a bounded set of initial conditions over bounded time…
This note states and proves an integral representation formula of the ``variation-of-constant'' type for continuous solutions of linear non-autonomous difference delay systems, in terms of a Lebesgue-Stieltjes integral involving a…
Results on continuous dependence on parameters, as well as on regularization, of solutions to linear systems of parabolic partial differential equations of second order with delay are given. One of the main features is that the topology on…
We obtain a result on the behavior of the solutions of a general nonautonomous Hopfield neural network model with delay, assuming some general bound for the product of consecutive terms in the sequence of neuron charging times and some…
The purpose of this paper is to establish Picard-Lindel\"{o}f theorem for local uniqueness and existence results for first-order systems of nonlinear delay dynamic equations. In the linear case, we extend our results to global existence and…
In this report, we develop a semistability analysis framework for nonlinear systems with bounded time-varying delays with applications to stability analysis of multiagent dynamic networks with consensus protocols in the presence of unknown…
In our adjacent work, we developed a spectral comparison principle for compound cocycles generated by delay equations. It allows to derive frequency inequalities for the uniform exponential stability of such cocycles by means of their…
The Mackey--Glass equation, which was proposed to illustrate nonlinear phenomena in physiological control systems, is a classical example of a simple looking time delay system with very complicated behavior. Here we use a novel approach for…
We study invariance and monotonicity properties of Kunita-type stochastic differential equations in $\RR^d$ with delay. Our first result provides sufficient conditions for the invariance of closed subsets of $\RR^d$. Then we present a…
Stability of the zero solution plays an important role in the investigation of positive systems. In this note, we revisit the $\mu$-stability of positive nonlinear systems with unbounded time-varying delays. The system is modelled by…
Equations of motion with delays naturally emerge in the analysis of complex biological control systems which are organized around biochemically mediated feedback interactions. We study the properties of a Mackey-Glass-type nonlinear map…
This contribution presents two exponential stability criteria for linear systems with multiple pointwise and distributed delays. These results (necessary and sufficient conditions) are given in terms of the delay Lyapunov matrix and the…
We consider scalar delay differential equations $x'(t) = -\delta x(t) + f(t,x_t) (*)$ with nonlinear f satisfying a sort of negative feedback condition combined with a boundedness condition. The well known Mackey-Glass type equations,…
We provide explicit conditions for uniform stability, global asymptotic stability and uniform exponential stability for dynamic equations with a single delay and a nonnegative coefficient. Some examples on nonstandard time scales are also…
This article investigates the stability of pantograph delay differential equations, in which the delayed argument is proportional to the present time. We derive analytic criteria that partition the parameter plane into unstable,…
This paper proposes a unified approach for studying global exponential stability of a general class of switched systems described by time-varying nonlinear functional differential equations. Some new delay-independent criteria of global…