Nonlocality of Reaction-Diffusion Equations Induced by Delay: Biological Modeling and Nonlinear Dynamics

By Stephen A. Gourley, Joseph W.-H. So, Jianhong Wu. 2004

179 citations recorded by the source corpus.

Subfields: Computer Networks and Communications, Genetics, Public Health, Environmental and Occupational Health

View Paper: https://www.semanticscholar.org/paper/b1a4e3e4d7c60c8b628aefe399c28369a57e4745

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In Computer Networks and Communications

1. Yuan Lou
2. Junjie Wei
3. Shanshan Chen
4. Ming Mei
5. A. Jungel
6. Shangjiang Guo
7. Junping Shi

In Genetics

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In Public Health, Environmental and Occupational Health

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2. Junjie Wei
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6. Qifeng Zhang
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8. Ming Mei

Citations in the corpus

• Stability of non-monotone critical traveling waves for reaction-diffusion equations with time-delay (2015, methodology): “• Nicholson’s blowflies model [8,9,16,17,20,28]: The so-called Nicholson’s birth rate function (also called the Ricker’s type function) is b(v) = pve−av, a > 0, p > 0, (1.”
• Stability and Hopf bifurcation in a diffusive logistic population model with nonlocal delay effect (2012, unknown): “Instead, following the approach in [3,18–20], it is more reasonable to consider the diffusive logistic population model with nonlocal delay effect as follows: ⎧⎪⎨ ⎪⎩ ∂u(x, t) ∂t = d u(x, t)+ λu(x, t) ( 1− ∫”
• Hopf bifurcation in a delayed reaction-diffusion-advection population model (2017, background): “For models with the homogeneous Neumann boundary conditions, researchers were mainly concerned with the Hopf bifurcation near the constant positive equilibrium, see [9, 13, 15, 18, 19, 22, 26, 28, 31, 32] and the references therein.”
• Stability and bifurcation in a reaction-diffusion model with nonlocal delay effect (2015, background): “Though such nonlocal delay equations in mathematical biology have been studied extensively in the literature [1,2,4,5,7,10,12], to the best of our knowledge, the qualitative study of the nonlocal delay effect has not been found.”
• Diffusive and nondiffusive population models (2010, background): “[56] argue that diffusion and time delays are not independent of each other, since individuals may be at different points in space at past times.”