Results 71 to 80 of about 168,933 (177)
Oscillatory Turing Patterns in a Simple Reaction-Diffusion System [PDF]
, 2007 Turing suggested that, under certain conditions, chemicals can react and diffuse in such a way as to produce steady-state inhomogeneous spatial patterns of chemical concentrations.
Liaw, S. S., Liu, R. T., Maini, P. K.
core
Stationary localized structures and the effect of the delayed feedback in the Brusselator model
, 2018 The Brusselator reaction-diffusion model is a paradigm for the understanding of dissipative structures in systems out of equilibrium. In the first part of this paper, we investigate the formation of stationary localized structures in the Brusselator ...
Averlant, Etienne +8 more
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Spatial Complexity of a Predator-Prey Model with Holling-Type Response
Abstract and Applied Analysis, 2014 We focus on a spatially extended Holling-type IV predator-prey model that contains some important factors, such as noise (random fluctuations), external periodic forcing, and diffusion processes.
Lei Zhang, Zhibin Li
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Electronic Journal of Qualitative Theory of Differential Equations, 2019 The ratio-dependent predator–prey model exhibits rich interesting dynamics due to the singularity of the origin. It is one of prototypical pattern formation models.
Wanjun Li, Xiaoyan Gao, Shengmao Fu
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Nonlinear Analysis, 2022 It is well known that integer-order neural networks with diffusion have rich spatial and temporal dynamical behaviors, including Turing pattern and Hopf bifurcation.
Jiazhe Lin, Jiapeng Li, Rui Xu
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, 2011 Competition of spatial and temporal instabilities under time delay near the codimension-two Turing-Hopf bifurcations is studied in a reaction-diffusion equation.
Hui-Juan Wang +4 more
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The spatial dynamics of a zebrafish model with cross-diffusions
Mathematical Biosciences and Engineering, 2017 This paper investigates the spatial dynamics of a zebrafish model with cross-diffusions. Sufficient conditions for Hopf bifurcation and Turing bifurcation are obtained by analyzing the associated characteristic equation.
Hongyong Zhao, Qianjin Zhang, Linhe Zhu
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Nonlocal control of pulse propagation in excitable media
, 2014 We study the effects of nonlocal control of pulse propagation in excitable media. As a generic example for an excitable medium the FitzHugh-Nagumo model with diffusion in the activator variable is considered. Nonlocal coupling in form of an integral term
Bachmair, Clemens A., Schöll, Eckehard
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Journal of Applied Mathematics, 2014 We revisit a homogeneous reaction-diffusion Turing model subject to the Neumann boundary conditions in the one-dimensional spatial domain. With the help of the Hopf bifurcation theory applicable to the reaction-diffusion equations, we are capable of ...
Yan Zhang, Zhenhua Bao
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Turing-Hopf Bifurcation and Spatio-Temporal Patterns of a Ratio-Dependent Holling-Tanner Model with Diffusion [PDF]
International Journal of Bifurcation and Chaos in Applied Sciences and Engineering, 2017 In this paper, the dynamics of a diffusive ratio-dependent Holling–Tanner model subject to Neumann boundary conditions is considered. We derive the conditions for the existence of Hopf, Turing, Turing–Hopf, Turing–Turing, Hopf-double-Turing and triple ...
Qi An, Weihua Jiang
semanticscholar +1 more source