Related papers: Mapping dynamical systems with distributed time de…
The evolution of networks of coupled chaotic maps with delayed interactions can be studied in the usual way by analyzing the evolution of the state of elements at each iteration time (the "Simulator" point of view), or it can be analyzed…
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 present a detailed study of a scalar differential equation with threshold state-dependent delayed feedback. This equation arises as a simplification of a gene regulatory model. There are two monotone nonlinearities in the model: one…
External and internal factors may cause a system's parameter to vary with time before it stabilizes. This drift induces a regime shift when the parameter crosses a bifurcation. Here, we study the case of an infinite dimensional system: a…
In this paper, we consider a general single population model with delay and patch structure, which could model the population loss during the dispersal. It is shown that the model admits a unique positive equilibrium when the dispersal rate…
A proper discretization of the logistic differential equation, which is preserving these two distinct equilibrium solutions and their unstability and stability, suggest that we need to examine the time delay of the logistic map. According…
We consider wave propagation in a complex structure coupled to a finite number $N$ of scattering channels, such as chaotic cavities or quantum dots with external leads. Temporal aspects of the scattering process are analysed through the…
This paper presents a novel dynamic coverage control algorithm allowing a group of robots to track an optimal-deployment configuration for arbitrary time-varying density functions. Building on singular perturbation theory, the proposed…
Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation. The time delay changes remarkably the oscillation frequency, the intrinsic…
In complex systems, external parameters often determine the phase in which the system operates, i.e., its macroscopic behavior. For nearly a century, statistical physics has extensively studied systems' transitions across phases,…
Subdiffusion on graphs is often modeled by time-fractional diffusion equations, yet its structural and dynamical consequences remain unclear. We show that subdiffusive transport on graphs is a memory-driven process generated by a random…
We study networks of theta neurons arranged on a ring with delayed interactions. In the continuum limit the systems are described by next generation neural field models with delays. We consider distributed delays with both finite and…
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…
Dynamic systems described by differential equations often involve feedback among system components. When there are time delays for components to sense and respond to feedback, delay differential equation (DDE) models are commonly used. This…
We investigate the dynamics of a single breathing localized structure in a three-component reaction-diffusion system subjected to the time-delayed feedback. We show that variation of the delay time and the feedback strength can lead either…
This chapter presents a dynamical systems point of view of the study of systems with delays. The focus is on how advanced tools from bifurcation theory, as implemented for example in the package DDE-BIFTOOL, can be applied to the study of…
A one species time-delay reaction-diffusion system defined on a complex networks is studied. Travelling waves are predicted to occur as follows a symmetry breaking instability of an homogenous stationary stable solution, subject to an…
One of the most salient spatio-temporal patterns in population ecology is the synchronization of fluctuating local populations across vast spatial extent. Synchronization of abundance has been widely observed across a range of spatial…
We develop and analyze mathematical models for residential burglary that incorporates police deployment through a delayed feedback mechanism. Motivated by empirical observations from publicly available crime and policing data, we extend a…
Periodic patterns in dynamical behaviours of biological models described by simple form differential delay equations are studied. Mathematical models are given by a class of scalar delay differential equations with a multiplicative time…