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A diffusive epidemic model with an infection-dependent recovery rate is formulated in this paper. Multiple constant steady states and spatially homogeneous periodic solutions are first proven by bifurcation analysis of the reaction…

Dynamical Systems · Mathematics 2025-09-12 Wael El Khateeb , Chanaka Kottegoda , Chunhua Shan

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 paper, we derive the algorithm for calculating the normal form of the double Hopf bifurcation that appears in a memory-based diffusion system via taking memory-based diffusion coefficient and the memory delay as the perturbation…

Dynamical Systems · Mathematics 2022-02-10 Yongli Song , Yahong Peng , Tonghua Zhang

In this paper, by incorporating the general delay to the reaction term in the memory-based diffusive system, we propose a diffusive system with memory delay and general delay (e.g., digestion, gestation, hunting, migration and maturation…

Analysis of PDEs · Mathematics 2022-03-22 Yehu Lv

We study the effects of discrete, randomly distributed time delays on the dynamics of a coupled system of self-propelling particles. Bifurcation analysis on a mean field approximation of the system reveals that the system possesses patterns…

Pattern Formation and Solitons · Physics 2015-06-05 Luis Mier-y-Teran-Romero , Brandon Lindley , Ira B. Schwartz

The stability of functional differential equations under delayed feedback is investigated near a Hopf bifurcation. Necessary and sufficient conditions are derived for the stability of the equilibrium solution using averaging theory. The…

Classical Analysis and ODEs · Mathematics 2008-12-31 Fatihcan M. Atay

Effects of immune delay on symmetric dynamics are investigated within a model of antigenic variation in malaria. Using isotypic decomposition of the phase space, stability problem is reduced to the analysis of a cubic transcendental…

Chaotic Dynamics · Physics 2012-09-21 K. B. Blyuss , Y. N. Kyrychko

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

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

In this work we prove occurrence of a super-critical Hopf bifurcation in a model of white blood cell formation structured by three maturation stages. We provide an explicit analytical expression for the bifurcation point depending on model…

Dynamical Systems · Mathematics 2019-10-24 Franziska Knauer , Thomas Stiehl , Anna Marciniak-Czochra

An epidemic model with distributed time delay is derived to describe the dynamics of infectious diseases with varying immunity. It is shown that solutions are always positive, and the model has at most two steady states: disease-free and…

Chaotic Dynamics · Physics 2012-09-21 K. B. Blyuss , Y. N. Kyrychko

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 a diffusive predator-prey model by incorporating the fear effect into prey population, since the fear of predators could visibly reduce the reproduction of prey. By introducing the mature delay as bifurcation parameter, we…

Dynamical Systems · Mathematics 2019-05-01 Daifeng Duan , Ben Niu , Junjie Wei

This paper concerns a free boundary problem modeling tumor growth with angiogenesis and two time delays. The two delays represent the time taken for cells to undergo mitosis and modify the rate of cell loss because of apoptosis,…

Analysis of PDEs · Mathematics 2022-01-05 Haihua Zhou , Zejia Wang , Daming Yuan , Huijuan Song

Diffusion-induced turbulence in spatially extended oscillatory media near a supercritical Hopf bifurcation can be controlled by applying global time-delay autosynchronization. We consider the complex Ginzburg-Landau equation in the…

Chaotic Dynamics · Physics 2009-11-10 C. Beta , A. S. Mikhailov

In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation…

Dynamical Systems · Mathematics 2019-01-30 Yanfei Du , Ben Niu , Junjie Wei

Logistic functions are good models of biological population growth. They are also popular in marketing in modelling demand-supply curves and in a different context, to chart the sales of new products over time. Delays being inherent in any…

Populations and Evolution · Quantitative Biology 2012-11-30 Milind M. Rao , K. L. Preetish

We consider an ecological model consisting of two species of predators competing for their common prey with explicit interference competition. With a proper rescaling, the model is portrayed as a singularly perturbed system with one-fast…

Dynamical Systems · Mathematics 2022-09-23 Susmita Sadhu

We focus on the qualitative analysis of a reaction-diffusion with spatial heterogeneity. The system is a generalization of the well known FitzHugh-Nagumo system in which the excitability parameter is space dependent. This heterogeneity…

Dynamical Systems · Mathematics 2017-06-28 B. Ambrosio

For delayed reaction-diffusion Schnakenberg systems with Neumann boundary conditions, critical conditions for Turing instability are derived, which are necessary and sufficient. And existence conditions for Turing, Hopf and Turing-Hopf…

Dynamical Systems · Mathematics 2020-01-08 Weihua Jiang , Hongbin Wang , Xun Cao