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We analyze the stabilization of unstable steady states by delayed feedback control with a periodic time-varying delay in the regime of a high-frequency modulation of the delay. The average effect of the delayed feedback term in the control…
Anticipated synchronisation occurs when a driven dynamical system synchronises with the future state of the driver system to which it is unidirectionally coupled. Previous theoretical and experimental studies have focused on setups with a…
Time delays pose an important challenge in networked control systems, which are now ubiquitous. Focusing on switched systems, we introduce a framework that provides an upper bound for errors caused by switching delays. Our framework is…
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…
Motivated by interest in providing more efficient services in customer service systems, we use statistical learning methods and delay history information to predict the conditional distribution of the customers' waiting times in queueing…
Oscillation of macroscopic variables is discovered in a metastable state in the Hamiltonian dynamical system of mean field XY model, the duration of which is divergent with the system size. This long-lasting periodic or quasiperiodic…
This work considers stochastic operators in general inner-product spaces, and in particular, systems with stochastically time-varying input delays of a known probability distribution. Stochastic dissipativity and stability are defined from…
We consider the stochastic patterns of a system of communicating, or coupled, self-propelled particles in the presence of noise and communication time delay. For sufficiently large environmental noise, there exists a transition between a…
Networks of coupled phase oscillators are one of the most studied dynamical systems with numerous applications in physics, chemistry, biology, and engineering. Their behaviour is often characterized by the emergence of various partially…
Quasi steady state assumptions are often used to simplify complex systems of ordinary differential equations in modelling of biochemical processes. The simplified system is designed to have the same qualitative properties as the original…
A delay is known to induce multistability in periodic systems. Under influence of noise, coupled oscillators can switch between coexistent orbits with different frequencies and different oscillation patterns. For coupled phase oscillators…
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…
In real-world networks the interactions between network elements are inherently time-delayed. These time-delays can not only slow the network but can have a destabilizing effect on the network's dynamics leading to poor performance. The…
It is known that an identical delay in all transmission lines can destabilize macroscopic stationarity of a neural network, causing oscillation or chaos. We analyze the collective dynamics of a network whose intra-transmission delays are…
Dynamical systems driven by strong external signals are ubiquituous in nature and engineering. Here we study "echo state networks", networks of a large number of randomly connected nodes, which represent a simple model of a neural network,…
Oscillations between swing modes of electric machines is an important limitation in achieving a high level of transient performance and reliability in power grids. Based on the new advances in measurement and transmission of wide-area…
Real-world systems can be strongly influenced by time delays occurring in self-coupling interactions, due to unavoidable finite signal propagation velocities. When the delays become significantly long, complicated high-dimensional phenomena…
The Frimmer-Novotny model to simulate two-level systems by coupled oscillators is extended by incorporating a constant time delay in the coupling. The effects of the introduced delay on system dynamics and two-level modeling are then…
In this paper, we investigate synchronization of coupled second-order linear harmonic oscillators with random noises and time delays. The interaction topology is modeled by a weighted directed graph and the weights are perturbed by white…
Synaptic, dendritic and single-cell kinetics generate significant time delays that shape the dynamics of large networks of spiking neurons. Previous work has shown that such effective delays can be taken into account with a rate model…