Related papers: Time-delayed nonlocal response induces traveling l…
It is known from both theory and experiments that introducing time delays into the communication network of mobile-agent swarms produces coherent rotational patterns. Often such spatio-temporal rotations can be bistable with other swarming…
In this paper, we focus on the existence of propagation fronts, solutions to non-local dispersion reaction models. Our aim is to provide a unified proof of this existence in a very broad framework using simple real analysis tools. In…
Data-driven methods for the identification of the governing equations of dynamical systems or the computation of reduced surrogate models play an increasingly important role in many application areas such as physics, chemistry, biology, and…
Excitable waves arise in many spatially-extended systems of either biological, chemical, or physical nature due to the interplay between local reaction and diffusion processes. Here we demonstrate that similar phenomena are encoded in the…
In this paper, a brief review of delay population models and their applications in ecology is provided. The inclusion of diffusion and nonlocality terms in delay models has given more capabilities to these models enabling them to capture…
We study the synchronization of a linear array of globally coupled identical logistic maps. We consider a time-delayed coupling that takes into account the finite velocity of propagation of the interactions. We find globally synchronized…
We consider the two-component delay system $\varepsilon x^{\prime}(t)=-x(t)-y(t)+f(x(t-1)),$ $y^{\prime}(t)=\eta x(t)$ with small parameters $\varepsilon,\eta$, and positive feedback function $f$. Previously, such systems have been reported…
Based on dynamical density functional theory (DDFT) we consider a non-equilibrium system of interacting colloidal particles driven by a constant tilting force through a periodic, symmetric "washboard" potential. We demonstrate that, despite…
We present a rigorous framework for the local analysis of canards and slow passages through bifurcations in a wide class of infinite-dimensional dynamical systems with time-scale separation. The framework is applicable to models where an…
We identify a new mechanism for propagation into unstable states in spatially extended systems, that is based on resonant interaction in the leading edge of invasion fronts. Such resonant invasion speeds can be determined solely based on…
We study the stability of unstable steady states in scalar retarded time-delayed systems subjected to a variable-delay feedback control. The important aspect of such a control problem is that time-delayed systems are already…
We consider the effects of a Mexican-hat-shaped nonlocal spatial coupling, i.e., symmetric long-range inhibition superimposed with short-range excitation, upon front propagation in a model of a bistable reaction-diffusion system. We show…
In this paper, we revisit a "relatively local" model proposed in arXiv:1811.07241, where locality and dimensionality of space only emerges from the entanglement structure of the state the system is in. Various quantities such as butterfly…
We discuss the relation between entanglement and nonlocality in the hidden nonlocality scenario. Hidden nonlocality signifies nonlocality that can be activated by applying local filters to a particular state that admits a local…
Time delay based control, recently proposed for non-collocated fourth-order systems, has several advantages over an observer-based state-feedback compensation of the low-damped oscillations in output. In this paper, we discuss a practical…
We investigate delay effects on dominant transition pathways (DTP) between metastable states of stochastic systems. A modified version of the Maier-Stein model with linear delayed feedback is considered as an example. By a stability…
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…
Based on methods of numerical simulation, the constructive role of nonlocal coupling is demonstrated in the context of wavefront propagation observed in an ensemble of overdamped bistable oscillators. Firstly, it is shown that the wavefront…
We analyze the implication of tristability on localization phenomena in one-dimensional extended dissipative systems. In this context, localized states appear due to the interaction and locking of front waves connecting different extended…
Self-activation coupled to a transport mechanism results in traveling waves that describe polymerization reactions, forest fires, tumor growth, and even the spread of epidemics. Diffusion is a simple and commonly used model of particle…