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We propose a new simple three-dimensional continuous autonomous model with two nonlinear terms and observe the dynamical behavior with respect to system parameters. This system changes the stability of fixed point via Hopf bifurcation and…
We consider a system of several nonlinear equations with a distributed delay and obtain absolute asymptotic stability conditions, independent of the delay. The ideas of the proofs are based on the notion of a strong attractor. The results…
This paper studies the problem of passive grasp stability under an external disturbance, that is, the ability of a grasp to resist a disturbance through passive responses at the contacts. To obtain physically consistent results, such a…
We study the possibility to stabilize unstable steady states and unstable periodic orbits in chaotic fractional-order dynamical systems by the time-delayed feedback method. By performing a linear stability analysis, we establish the…
In this paper, we consider the stability analysis of large-scale distributed networked control systems with random communication delays between linearly interconnected subsystems. The stability analysis is performed in the Markov jump…
Time-delayed feedback methods can be used to control unstable periodic orbits as well as unstable steady states. We present an application of extended time delay autosynchronization introduced by Socolar et al. to an unstable focus. This…
We consider the Ricker model with delay and constant or periodic stocking. We found that the high stocking density tends to neutralize the delay effect on stability. Conditions are established on the parameters to ensure the global…
Delays are ubiquitous in applied problems, but often do not arise as the simple constant discrete delays that analysts and numerical analysts like to treat. In this chapter we show how state-dependent delays arise naturally when modeling…
Mathematical models of glucose, insulin, and pancreatic $\beta$-cell mass dynamics are essential for understanding the physiological basis of type 2 diabetes. This paper investigates the Topp model's discrete-time dynamics to represent…
We consider abstract evolution equations with on-off time delay feedback. Without the time delay term, the model is described by an exponentially stable semigroup. We show that, under appropriate conditions involving the delay term, the…
This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing…
Motivated by the regulator theory and adaptive controls, several notions on output stability in the framework of input-to-state stability (iss) were introduced for finite-dimensional systems. It turned out that these output stability…
We study the 1d swarmalator model augmented with time delayed coupling. Along with the familiar sync, async, and phase wave states, we find a family of unsteady states where the order parameters are time periodic, sometimes with clean…
In this paper, we investigate a class of non-monotone reaction-diffusion equations with distributed delay and a homogenous boundary Neumann condition, which have a positive steady state. The main concern is the global attractivity of the…
We study the dynamics of a piecewise-linear second-order delay differential equation that is representative of feedback systems with relays (switches) that actuate after a fixed delay. The system under study exhibits strong…
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…
In this paper we consider the global stability of solutions of an affine stochastic differential equation. The differential equation is a perturbed version of a globally stable linear autonomous equation with unique zero equilibrium where…
The problem considered in the paper is exponential stability of linear equations and global attractivity of nonlinear non-autonomous equations which include a non-delay term and one or more delayed terms. First, we demonstrate that…
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.
In this paper, we study the asymptotic behavior of solutions to a scalar fractional delay differential equations around the equilibrium points. More precise, we provide conditions on the coefficients under which a linear fractional delay…