Related papers: Stability in a scalar differential equation with m…

Simple form scalar differential equation with delay and nonlinear negative periodic feedback is considered. The existence of several types of slowly oscillating periodic solutions is shown with the same and double periods of the feedback…

This work is the first attempt to treat partial differential equations with discrete (concentrated) state-dependent delay. The main idea is to approximate the discrete delay term by a sequence of distributed delay terms (all with…

In this paper we study, at different levels of generality, certain systems of delay differential equations (DDE). One focus and motivation is a system with state-dependent delay (SD-DDE) that has been formulated to describe the maturation…

Stability of linear systems with uncertain bounded time-varying delays is studied under assumption that the nominal delay values are not equal to zero. An input-output approach to stability of such systems is known to be based on the bound…

This paper deals with the boundary stabilization problem of a one-dimensional wave equation with a switching time-delay in the boundary. We show that the problem is well-posed in the sense of semigroups theory of linear operators. Then, we…

This paper deals with stability of discrete-time switched linear systems whose all subsystems are unstable. We present sufficient conditions on the subsystems matrices such that a switched system is globally exponentially stable under a set…

Stability is required for real world controlled systems as it ensures that those systems can tolerate small, real world perturbations around their desired operating states. This paper shows how stability for continuous systems modeled by…

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,…

We provide a systematic approach to stable central limit theorems for d-dimensional martingale difference arrays and martingale difference sequences. The conditions imposed are straightforward extensions of the univariate case.

In this paper, we study both the oscillation and the stability of impulsive differential equations when not only the continuous argument but also the impulse condition involves delay. The results obtained in the present paper improve and…

This article deals with stabilizing discrete-time switched linear systems. Our contributions are threefold: Firstly, given a family of linear systems possibly containing unstable dynamics, we propose a large class of switching signals that…

A two-dimensional system of differential equations with delay modelling the glucose-insulin interaction processes in the human body is considered. Sufficient conditions are derived for the unique positive equilibrium in the system to be…

We consider the existence and stability of static configurations of a scalar field in a five dimensional spacetime in which the extra spatial dimension is compactified on an $S^1/Z_2$ orbifold. For a wide class of potentials with multiple…

For the fractional order systems \[D^\alpha x(t)=f(x),\quad 0<\alpha\leq 1,\] one can have a critical value of $\alpha$ viz $\alpha_*$ such that the system is stable for $0<\alpha<\alpha_*$ and unstable for $\alpha_*<\alpha\leq 1$. In…

This paper deals with the stability of linear periodic difference delay systems, where the value at time $t$ of a solution is a linear combination with periodic coefficients of its values at finitely many delayed instants…

We derive an exact solution for a simple non-autonomous delay differential equation (DDE) over the entire real-time axis, representing it as a sum of Gaussian-shaped dynamics with distinct peak positions. This marks the first explicit…

We show that delay-differential equations (DDE) exhibit universal bifurcation scenarios, which are observed in large classes of DDEs with a single delay. Each such universality class has the same sequence of stabilizing or destabilizing…

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…

The objective of this paper is to investigate the stability of limit cycles of a mathematical model with a distributed delay which describes the interaction between p53 and mdm2. Choosing the delay as a bifurcation parameter we study the…

For given non-consistent initial conditions, we study the stability of a class of generalised linear systems of difference equations with constant coefficients and taking into account that the leading coefficient can be a singular matrix.…