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In this paper, we consider the dynamics of a delayed reaction-diffusion mussel-algae system subject to Neumann boundary conditions. When the delay is zero, we show the existence of positive solutions and the global stability of the boundary…

Dynamical Systems · Mathematics 2019-10-23 Zuolin Shen , Junjie Wei

We explore both analytically and numerically an ensemble of coupled phase-oscillators governed by a Kuramoto-type system of differential equations. However, we have included the effects of time-delay (due to finite signal-propagation…

Adaptation and Self-Organizing Systems · Physics 2015-06-16 Liam Timms , Lars Q. English

Double Hopf bifurcation analysis can be used to reveal some complicated dynamical behavior in a dynamical system, such as the existence or coexistence of periodic orbits, quasi-periodic orbits, or even chaos. In this paper, an algorithm for…

Dynamical Systems · Mathematics 2018-11-27 Yanfei Du , Ben Niu , Yuxiao Guo , Junjie Wei

This study investigates the impact of delayed coupling on the global and local synchronization of identical coupled oscillators residing in a ring. Utilizing the Kuramoto model, we examine the effects of delayed coupling on collective…

Adaptation and Self-Organizing Systems · Physics 2025-02-04 Sara Ameli , Esmaeil Mahdavi , Mina Zarei , Farhad Shahbazi

By means of numerical integration we investigate the coherent and incoherent phases in a generalized Kuramoto model of phase-coupled oscillators with distance-dependent delay. Preserving the topology of a complete graph, we arrange the…

Chaotic Dynamics · Physics 2010-08-04 Karol Trojanowski , Lech Longa

This paper focuses on the delay induced Hopf bifurcation in a dual model of Internet congestion control algorithms which can be modeled as a time-delay system described by a one-order delay differential equation (DDE). By choosing…

Networking and Internet Architecture · Computer Science 2007-12-27 Dawei Ding , Jie Zhu , Xiaoshu Luo , Yuliang Liu

This study examines the complex interplay between inertia and time delay in regular rotor networks within the framework of the second-order Kuramoto model. By combining analytical and numerical methods, we demonstrate that intrinsic time…

Adaptation and Self-Organizing Systems · Physics 2025-12-19 Esmaeil Mahdavi , Mina Zarei , Philipp Hövel , Farhad Shahbazi

The Kuramoto model has shaped our understanding of synchronization in complex systems, yet its phase-only formulation neglects amplitude dynamics that are intrinsic to many oscillatory networks. In this work, we revisit Kuramoto-type…

Dynamical Systems · Mathematics 2026-01-16 Kuan-Wei Chen , Ting-Yang Hsiao

The Kuramoto model of coupled second order damped oscillators on convergent sequences of graphs is analyzed in this work. The oscillators in this model have random intrinsic frequencies and interact with each other via nonlinear coupling.…

Dynamical Systems · Mathematics 2021-11-29 Hayato Chiba , Georgi S. Medvedev

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

In this work we propose a feedback approach to regulate the chaotic behavior of the whole family of the generalized Lorenz system, by designing a nonlinear delayed feedback control. We first study the effect of the delay on the dynamics of…

Mathematical Physics · Physics 2015-01-05 Rachele Barresi , Maria Carmela Lombardo , Marco Sammartino

We study the mean-field limit of the Kuramoto model of globally coupled oscillators. By studying the evolution in Fourier space and understanding the domain of dependence, we show a global stability result. Moreover, we can identify…

Analysis of PDEs · Mathematics 2025-03-25 Helge Dietert

We investigate the steady-state solution and its bifurcations in time-delay systems with band-limited feedback. This is a first step in a rigorous study concerning the effects of AC-coupled components in nonlinear devices with time-delayed…

Chaotic Dynamics · Physics 2009-11-11 Lucas Illing , Daniel J. Gauthier

In this work, we analyze the Kuramoto model (KM) with inertia on a convergent family of graphs. It is assumed that the intrinsic frequencies of the individual oscillators are sampled from a probability distribution. In addition, a given…

Pattern Formation and Solitons · Physics 2023-07-26 Hayato Chiba , Georgi S. Medvedev , Matthew S. Mizuhara

The Kuramoto model is a system of ordinary differential equations for describing synchronization phenomena defined as a coupled phase oscillators. In this paper, a bifurcation structure of the infinite dimensional Kuramoto model is…

Dynamical Systems · Mathematics 2019-02-20 Hayato Chiba

We study the synchronization of a small-world network of identical coupled phase oscillators with Kuramoto interaction. First, we consider the model with instantaneous mutual interaction and the normalized coupling constant to the degree of…

Disordered Systems and Neural Networks · Physics 2017-05-23 Sara Ameli , Farhad Shahbazi , Maryam Karimian , Tahereh Malakoutikhah

In recent years there has been an increasing interest in studying time-delayed coupled networks of oscillators since these occur in many real life applications. In many cases symmetry patterns can emerge in these networks, as a consequence…

Dynamical Systems · Mathematics 2014-07-31 Diego Paolo Ferruzzo Correa , Claudia Wulff , Jose Roberto Castilho Piqueira

In this paper, we consider the Shigesada-Kawasaki-Teramoto (SKT) model, which presents cross-diffusion terms describing competition pressure effects. Even though the reaction part does not present the activator-inhibitor structure,…

Analysis of PDEs · Mathematics 2022-02-10 Cinzia Soresina

The Kuramoto phase diffusion equation is a nonlinear partial differential equation which describes the spatio-temporal evolution of a phase variable in an oscillatory reaction diffusion system. Synchronization manifests itself in a…

Disordered Systems and Neural Networks · Physics 2009-03-30 Ralf Toenjes , Bernd Blasius

We study transitions in the Kuramoto model by shedding light on asymmetry in the natural frequency distribution, which has been assumed to be symmetric in many previous studies. The asymmetry brings two nonstandard bifurcation diagrams,…

Adaptation and Self-Organizing Systems · Physics 2017-02-01 Yu Terada , Keigo Ito , Toshio Aoyagi , Yoshiyuki Y. Yamaguchi