Normal form and Hopf bifurcation for the memory‐based reaction‐diffusion equation with nonlocal effect
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DOI: 10.1002/mma.10185
Abstract: In this paper, we provide the normal form for the Hopf bifurcation of a class of the reaction‐diffusion equation with memory‐based diffusion and nonlocal effect, where the delay is present in the differential term, similar… read more here.
Keywords: normal form; hopf bifurcation; diffusion; bifurcation ... See more keywords
Global asymptotical stability and Hopf bifurcation for a three‐species Lotka‐Volterra food web model
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DOI: 10.1002/mma.10376
Abstract: In this article, we consider a delayed three‐species Lotka‐Volterra food web model with diffusion and homogeneous Neumann boundary conditions. We proved that the positive constant equilibrium solution is globally asymptotically stable for the system without… read more here.
Keywords: bifurcation; three species; hopf bifurcation; model ... See more keywords
Hopf bifurcation analysis of a two‐delayed diffusive predator–prey model with spatial memory of prey
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DOI: 10.1002/mma.10416
Abstract: In this paper, we consider a diffusive predator–prey model with spatial memory of prey and gestation delay of predator. For the system without delays, we study the stability of the positive equilibrium in the case… read more here.
Keywords: bifurcation; prey; diffusive predator; hopf bifurcation ... See more keywords
Critical diapause portion for oscillations: Parametric trigonometric functions and their applications for Hopf bifurcation analyses
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DOI: 10.1002/mma.5424
Abstract: An important adaptive mechanism for ticks in respond to variable climate is diapause. Incorporating this physiological mechanism into a tick population dynamics model results in a delay differential system with multiple delays. Here, we consider… read more here.
Keywords: diapause portion; trigonometric functions; hopf bifurcation; parametric trigonometric ... See more keywords
Delay‐included Turing‐Hopf bifurcation in the diffusive mussel‐algae model
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DOI: 10.1002/mma.7290
Abstract: In this paper, the main content is the consideration of the dynamics of a diffusive mussel‐algae model with delay subject to Neumann boundary condition. We will analyze the corresponding characteristic equation and study the existence… read more here.
Keywords: mussel algae; diffusive mussel; turing hopf; bifurcation ... See more keywords
Flow-induced oscillations via Hopf bifurcation in a fluid–solid interaction problem
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DOI: 10.1007/s00208-025-03179-6
Abstract: We furnish necessary and sufficient conditions for the occurrence of local Hopf bifurcation in a notably significant fluid–structure problem, where a Navier–Stokes liquid interacts with a rigid body that is subject to an undamped elastic… read more here.
Keywords: problem; documentclass 12pt; document; hopf bifurcation ... See more keywords
Hopf bifurcation in an age-structured predator–prey system with Beddington–DeAngelis functional response and constant harvesting
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DOI: 10.1007/s00285-024-02070-3
Abstract: In this paper, an age-structured predator–prey system with Beddington–DeAngelis (B–D) type functional response, prey refuge and harvesting is investigated, where the predator fertility function f(a) and the maturation function β(a)\documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy}… read more here.
Keywords: system; predator; bifurcation; document ... See more keywords
Global Hopf Bifurcation for Differential-Algebraic Equations with State-Dependent Delay
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DOI: 10.1007/s10884-017-9640-0
Abstract: We develop a global Hopf bifurcation theory for differential equations with a state-dependent delay governed by an algebraic equation, using the $$S^1$$S1-equivariant degree. We apply the global Hopf bifurcation theory to a model of genetic… read more here.
Keywords: state; global hopf; state dependent; dependent delay ... See more keywords
Stability and Double-Hopf Bifurcations of a Gause–Kolmogorov-Type Predator–Prey System with Indirect Prey-Taxis
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DOI: 10.1007/s10884-020-09878-9
Abstract: In this paper, we deal with the Gause–Kolmogorov-type predator–prey system with indirect prey-taxis, which means that directional movement of predators is stimulated by some chemicals emitted by preys. The existence of the positive equilibrium, the… read more here.
Keywords: prey; indirect prey; double hopf; hopf bifurcation ... See more keywords
Hopf Bifurcation for General 1D Semilinear Wave Equations with Delay
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DOI: 10.1007/s10884-021-10009-1
Abstract: We consider boundary value problems for 1D autonomous damped and delayed semilinear wave equations of the type $$\begin{aligned} \partial ^2_tu(t,x)- a(x,\lambda )^2\partial _x^2u(t,x)= b(x,\lambda ,u(t,x),u(t-\tau ,x),\partial _tu(t,x),\partial _xu(t,x)), \; x \in (0,1) \end{aligned}$$ ∂ t… read more here.
Keywords: general semilinear; hopf bifurcation; bifurcation general; semilinear wave ... See more keywords
Hopf Bifurcation in a Delayed Population Model Over Patches with General Dispersion Matrix and Nonlocal Interactions
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DOI: 10.1007/s10884-021-10070-w
Abstract: In this paper, we consider a single species population model over patches with delay and nonlocal interactions, for which no symmetry for the dispersion (connection) matrix is assumed. We show that there exists a positive… read more here.
Keywords: model patches; nonlocal interactions; model; dispersion ... See more keywords