Related papers: A Mean-Field Model for Extended Stochastic Systems…
We investigate the effects of a time-delayed all-to-all coupling scheme in a large population of oscillators with natural frequencies following a bimodal distribution. The regions of parameter space corresponding to synchronized 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…
We study the effects of delayed coupling on timing and pattern formation in spatially extended systems of dynamic oscillators. Starting from a discrete lattice of coupled oscillators, we derive a generic continuum theory for collective…
We investigated the effect of time delays on phase configurations in a set of two-dimensional coupled phase oscillators. Each oscillator is allowed to interact with its neighbors located within a finite radius, which serves as a control…
Time-delay systems are an important class of dynamical systems that provide a solid mathematical framework to deal with many application domains of interest. In this paper we focus on nonlinear control systems with unknown and time-varying…
We examine a system of N=2 coupled non-linear delay-differential equations representing financial market dynamics. In such time delay systems, coupled oscillations have been derived. We linearize the system for small time delays and study…
We consider networks of coupled stochastic oscillators. When coupled we find strong collective oscillations, while each unit remains stochastic. In the limit (N\to \infty) we derive a system of integro-delay equations and show analytically…
The time needed to exchange information in the physical world induces a delay term when the respective system is modeled by differential equations. Time delays are hence ubiquitous, being furthermore likely to induce instabilities and with…
Signal transmission delays tend to destabilize dynamical networks leading to oscillation, but their dispersion contributes oppositely toward stabilization. We analyze an integro-differential equation that describes the collective dynamics…
Inspired by the observation of a distributed time delay in the nonlinear response of an optical resonator, we investigate the effects of a similar delay on a noise-driven mechanical oscillator. For a delay time that is commensurate with the…
The Jensen inequality has been recognized as a powerful tool to deal with the stability of time-delay systems. Recently, a new inequality that encompasses the Jensen inequality was proposed for the stability analysis of systems with finite…
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 develop a generalized stability framework for stochastic discrete-time systems, where the generality pertains to the ways in which the distribution of the state energy can be characterized. We use tools from finance and operations…
The paper deals with the global asymptotic stability of general nonlinear time-delay systems with delay-dependent impulses through the Lyapunov-Krasovskii method. We derive a unified stability criterion which can be applied to a variety of…
We investigate the effects of delayed interactions on the stationary distribution of the noisy voter model. We assume that the delayed interactions occur through the periodic polling mechanism and replace the original instantaneous…
In systems of coupled oscillators, the effects of complex signaling can be captured by time delays and phase shifts. Here, we show how time delays and phase shifts lead to different oscillator dynamics and how synchronization rates can be…
We show that \emph{stochastic bursting} is observed in a ring of unidirectional delay-coupled noisy excitable systems, thanks to the combinational action of time-delayed coupling and noise. Under the approximation of timescale separation,…
Networks of neural mass nodes with delayed interactions are increasingly being used as models for large-scale brain activity. To complement the growing number of computational studies of such networks, it is timely to develop new…
In this paper, we propose a framework to investigate the collective dynamics in ensembles of globally coupled phase oscillators when higher-order modes dominate the coupling. The spatiotemporal properties of the attractors in various…
We study the noise delayed decay of unstable nonequilibrium states in nonlinear dynamical systems within the framework of the overdamped Brownian motion model. We give the exact expressions for the decay times of unstable states for…