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In a previous work we investigated the existence of Hopf degenerate bifurcation points for a differential delay equation modeling leukemia and we actually found Hopf points of codimension two for the considered problem. If around the…

Dynamical Systems · Mathematics 2012-08-16 Anca Veronica Ion , Raluca Mihaela Georgescu

In this paper, we investigate the dynamical behaviors of a delayed lateral vibration model of footbridges proposed based on the facts that pedestrians will reduce their walking speed or stop walking when the response of the footbridge…

Dynamical Systems · Mathematics 2025-03-05 Xuemei Li , Yechi Liu

We investigate the effect of time delay on the dynamical model of love. The local stability analysis proves that the time delay on the return function can cause a Hopf bifurcation and a cyclic love dynamics. The condition for the occurrence…

Chaotic Dynamics · Physics 2018-02-14 Woo-Sik Son , Young-Jai Park

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

It is known that Lotka - Volterra type differential equations with delays or distributed delays have an important role in modeling ecological systems. In this paper we study the effects of distributed delay on the dynamics of the harvested…

Dynamical Systems · Mathematics 2013-11-12 Chol Kim

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…

Pattern Formation and Solitons · Physics 2015-06-18 Svetlana V. Gurevich

We consider the effect of asymmetric temporal delays in a system of two coupled Hopfield neurons. For couplings of opposite signs, a limit cycle emerges via a supercritical Hopf bifurcation when the sum of the delays reaches a critical…

Biological Physics · Physics 2011-11-10 Sebastian F. Brandt , Axel Pelster , Ralf Wessel

This paper presents an investigation of the dynamics of two coupled non-identical FitzHugh-Nagumo neurons with quadratic term and delayed synaptic connection. We consider coupling strength and time delay as bifurcation parameters, and try…

Chaotic Dynamics · Physics 2016-02-29 Niloofar Farajzadeh Tehrani , MohammadReza Razvan

Delays and stochasticity have both served as crucially valuable ingredients in mathematical descriptions of control, physical, and biological systems. In this work, we investigate how explicitly dynamical stochasticity in delays modulates…

Molecular Networks · Quantitative Biology 2023-07-10 Bhargav R. Karamched , Christopher E. Miles

In this paper, a mathematical model of pneumococcal pneumonia with time delays is proposed. The stability theory of delay differential equations is used to analyze the model. The results show that the disease-free equilibrium is…

Populations and Evolution · Quantitative Biology 2019-01-16 Fulgensia Kamugisha Mbabazi , Joseph Y. T. Mugisha , Mark Kimathi

For many physical systems the transition from a stationary solution to sustained small amplitude oscillations corresponds to a Hopf bifurcation. For systems involving impacts, thresholds, switches, or other abrupt events, however, this…

Dynamical Systems · Mathematics 2019-05-07 David J. W. Simpson

We study scalar delay equations $$\dot{x} (t) = \lambda f(x(t-1)) + b^{-1} (x(t) + x(t -p/2))$$ with odd nonlinearity $f$, real nonzero parameters $\lambda, \, b$, and two positive time delays $1,\ p/2$. We assume supercritical…

Dynamical Systems · Mathematics 2018-02-20 Bernold Fiedler , Isabelle Schneider

Noise has significant impact on nonlinear phenomena. Here we demonstrate that, in opposition to previous assumptions, additive noise interfere with the linear stability of scalar nonlinear systems when these are subject to time delay. We…

Dynamical Systems · Mathematics 2015-06-15 Jérémie Lefebvre , Axel Hutt

Time-delay chaotic systems refer to the hyperchaotic systems with multiple positive Lyapunov exponents. It is characterized by more complex dynamics and a wider range of applications as compared to those non-time-delay chaotic systems. In a…

Dynamical Systems · Mathematics 2021-03-29 Erxi Zhu , Min Xu , Dechang Pi

We consider the scalar delayed differential equation $\ep\dot x(t)=-x(t)+f(x(t-r))$, where $\ep>0$, $r=r(x,\ep)$ and $f$ represents either a positive feedback $df/dx>0$ or a negative feedback $df/dx<0$. When the delay is a constant, i.e.…

Pattern Formation and Solitons · Physics 2012-03-20 Xavier Pellegrin , Clodoaldo Grotta Ragazzo , Coraci Malta , Khashayar Pakdaman

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 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…

Dynamical Systems · Mathematics 2026-04-10 Pragati Dutta , Sachin Bhalekar

Two complementary analyses of a cyclic negative feedback system with delay are considered in this paper. The first analysis applies the work by Sontag, Angeli, Enciso and others regarding monotone control systems under negative feedback,…

Molecular Networks · Quantitative Biology 2007-05-23 G. A. Enciso

In this work, we investigate the dynamical properties of a reaction-diffusion system arising from tumor-therapy modelling that features both nonlinear interactions and nonlocal delay. By applying the Lyapunov-Schmidt reduction, we establish…

Dynamical Systems · Mathematics 2025-12-17 Dandan Hu , Yuan Yuan

In this paper a stability analysis for a Cournot duopoly model with tax evasion and time-delay in a continuous-time framework is presented. The mathematical model under consideration follows a gradient dynamics approach, is nonlinear and…

Dynamical Systems · Mathematics 2021-03-05 Benjamín A. Itzá-Ortiz , Raúl Villafuerte-Segura , Eduardo Alvarado-Santos