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We consider the model of economic growth with time delayed investment function. Assuming the investment is time distributed we can use the linear chain trick technique to transform delay differential equation system to equivalent system of…

Theoretical Economics · Economics 2020-02-13 Luca Guerrini , Adam Krawiec , Marek Szydlowski

Networks of globally coupled, noise activated, bistable elements with connection time delays are considered. The dynamics of these systems is studied numerically using a Langevin description and analytically using (1) a Gaussian…

Statistical Mechanics · Physics 2009-11-11 Daniel Huber , Lev Tsimring

While synchronized states, and the dynamical pathways through which they emerge, are often regarded as the paradigm to understand the dynamics of information spreading on undirected networks of nonlinear dynamical systems, when we consider…

Adaptation and Self-Organizing Systems · Physics 2025-07-10 Giulio Colombini , Nicola Guglielmi , Armando Bazzani

Dynamics in delayed differential equations (DDEs) is a well studied problem mainly because DDEs arise in models in many areas of science including biology, physiology, population dynamics and engineering. The change of nature in the…

We study the completely synchronized states (CSSs) of a system of coupled logistic maps as a function of three parameters: interaction strength ($\varepsilon$), range of the interaction ($\alpha$), that can vary from first-neighbors to…

Chaotic Dynamics · Physics 2018-03-07 Celia Anteneodo , Juan Carlos Gonzalez-Avella , Raul O. Vallejos

Neural field models with transmission delay may be cast as abstract delay differential equations (DDE). The theory of dual semigroups (also called sun-star calculus) provides a natural framework for the analysis of a broad class of delay…

Dynamical Systems · Mathematics 2017-12-11 Stephan A. van Gils , Sebastiaan G. Janssens , Yuri A. Kuznetsov , Sid Visser

Parametric oscillators are examples of externally driven systems that can exhibit two stable states with opposite phase depending on the initial conditions. In this work, we propose to study what happens when the external forcing is…

Pattern Formation and Solitons · Physics 2024-02-13 Benjamin Apffel , Romain Fleury

In this paper, we investigate a reaction-diffusion-advection model with time delay effect. The stability/instability of the spatially nonhomogeneous positive steady state and the associated Hopf bifurcation are investigated when the given…

Dynamical Systems · Mathematics 2017-06-08 Shanshan Chen , Yuan Lou , Junjie Wei

We deal with a class of second order in time nonlinear evolution equations with state-dependent delay. This class covers several important PDE models arising in the theory ofnonlinear plates. Our first result states well-posedness in a…

Analysis of PDEs · Mathematics 2016-03-22 Igor Chueshov , Alexander Rezounenko

This paper studies the boundary output feedback stabilization of general 1-D reaction-diffusion PDEs in the presence of a state delay in the reaction term. The control input applies through a Robin boundary condition while the system output…

Optimization and Control · Mathematics 2021-06-01 Hugo Lhachemi , Robert Shorten

We present a study of a delay differential equation (DDE) model for the Mid-Pleistocene Transition (MPT). We investigate the behavior of the model when subjected to periodic forcing. The unforced model has a bistable region consisting of a…

Dynamical Systems · Mathematics 2019-01-14 Courtney Quinn , Jan Sieber , Anna von der Heydt

In this paper, we analyze the effect of optical feedback on the dynamics of a passively mode-locked ring laser operating in the regime of temporal localized structures. This laser system is modeled by a system of delay differential…

Pattern Formation and Solitons · Physics 2022-03-07 Thomas G. Seidel , Julien Javaloyes , Svetlana V. Gurevich

We study the periodic forced response of a system of two limit cycle oscillators that interact with each other via a time delayed coupling. Detailed bifurcation diagrams in the parameter space of the forcing amplitude and forcing frequency…

Chaotic Dynamics · Physics 2007-05-23 D. V. Ramana Reddy , A. Sen , G. L. Johnston

Systems of differential equations with state-dependent delay are considered. The delay dynamically depends on the state i.e. is governed by an additional differential equation. By applying the time transformations we arrive to constant…

Classical Analysis and ODEs · Mathematics 2017-06-29 A. V. Rezounenko

Local bifurcation theory typically deals with the response of a degenerate but isolated equilibrium state or periodic orbit of a dynamical system to perturbations controlled by one or more independent parameters, and characteristically uses…

Dynamical Systems · Mathematics 2010-02-23 D. R. J. Chillingworth , L. Sbano

We consider functional differential equations(FDEs) which are perturbations of smooth ordinary differential equations(ODEs). The FDE can involve multiple state-dependent delays or distributed delays (forward or backward). We show that,…

Dynamical Systems · Mathematics 2021-03-10 Jiaqi Yang , Joan Gimeno , Rafael de la Llave

A common task when analysing dynamical systems is the determination of normal forms near local bifurcations of equilibria. As most of these normal forms have been classified and analysed, finding which particular class of normal form one…

Dynamical Systems · Mathematics 2017-12-14 Jan Sieber

We propose an SDP-based framework to address the stabilization of input delay systems while taking into account dissipative constraints. A key to our approach is the introduction of the concept of parameterized linear dynamical state…

Optimization and Control · Mathematics 2025-12-02 Qian Feng , Cong Zhang , Bo Wei

We show that Pyragas delayed feedback control can stabilize an unstable periodic orbit (UPO) that arises from a generic subcritical Hopf bifurcation of a stable equilibrium in an n-dimensional dynamical system. This extends results of…

Chaotic Dynamics · Physics 2015-05-19 Genevieve Brown , Claire M. Postlethwaite , Mary Silber

A shifted or misaligned feedback loop gives rise to a two-point nonlocality that is the spatial analog of a temporal delay. Important consequences of this nonlocal coupling have been found both in diffusive and in diffractive systems, and…

Pattern Formation and Solitons · Physics 2015-05-18 Roberta Zambrini , Francesco Papoff