Related papers: Mapping dynamical systems with distributed time de…
High-dimensional chaos displayed by multi-component systems with a single time-delayed feedback is shown to be accessible to time series analysis of a scalar variable only. The mapping of the original dynamics onto scalar time-delay systems…
Delayed interactions are a common property of coupled natural systems and therefore arise in a variety of different applications. For instance, signals in neural or laser networks propagate at finite speed giving rise to delayed…
We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…
Time delays, modelling the process of intracellular gene expression, have been shown to have important impacts on the dynamics of pattern formation in reaction-diffusion systems. In particular, past work has shown that such time delays can…
A discrete delay is included to model the time between the capture of the prey and its conversion to viable biomass in the simplest classical Gause type predator-prey model that has equilibrium dynamics without delay. As the delay increases…
Time-delay systems are, in many ways, a natural set of dynamical systems for natural scientists to study because they form an interface between abstract mathematics and data. However, they are complicated because past states must be…
Delayed processes are ubiquitous throughout biology. These delays may arise through maturation processes or as the result of complex multi-step networks, and mathematical models with distributed delays are increasingly used to capture the…
A novel way of using neural networks to learn the dynamics of time delay systems from sequential data is proposed. A neural network with trainable delays is used to approximate the right hand side of a delay differential equation. We relate…
Absorption yields an additional exponential decay in open quantum systems which can be described by shifting the (scattering) energy E along the imaginary axis, E+i\hbar/2\tau_{a}. Using the random matrix approach, we calculate analytically…
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 spiking properties of a subcritical Hopf oscillator with a time delayed nonlinear feedback is investigated. Finite time delay is found to significantly affect both the statistics and the fine structure of the spiking behavior. These…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
Time delay in general leads to instability in some systems, while a specific feedback with delay can control fluctuated motion in nonlinear deterministic systems to a stable state. In this paper, we consider a non-stationary stochastic…
Nonlinear dynamical systems with time delay are abundant in applications, but are notoriously difficult to analyse and predict because delay-induced effects strongly depend on the form of the nonlinearities involved, and on the exact way…
A network of noisy bistable elements with global time-delayed couplings is considered. A dichotomous mean field model has recently been developed describing the collective dynamics in such systems with uniform time delays near the…
Delay differential equations (DDEs) with large delays play a pivotal role in understanding stability and bifurcations in systems ranging from neural networks to laser dynamics. While prior work has extensively studied DDEs with discrete…
This work concerns the dynamics of a certain class of delay differential equations (DDEs) which we refer to as state dependent delay maps. These maps are generated by delay differential equations where the derivative of the current state…
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 consider a network of delay dynamical systems connected in a ring via unidirectional positive feedback with constant delay in coupling. For the specific case of Mackey-Glass systems on the ring topology, we capture the phenomena of…
We consider the effect of distributed delays in neural feedback systems. The avian optic tectum is reciprocally connected with the nucleus isthmi. Extracellular stimulation combined with intracellular recordings reveal a range of signal…