Results 51 to 60 of about 32,500 (209)
Bifurcation and Patterns Analysis for a Spatiotemporal Discrete Gierer-Meinhardt System
Mathematics, 2022 The Gierer-Meinhardt system is one of the prototypical pattern formation models. The bifurcation and pattern dynamics of a spatiotemporal discrete Gierer-Meinhardt system are investigated via the couple map lattice model (CML) method in this paper.
Biao Liu, Ranchao Wu
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Turing Instability and Pattern Formation in an Activator-Inhibitor System with Nonlinear Diffusion
, 2014 In this work we study the effect of density dependent nonlinear diffusion on pattern formation in the Lengyel--Epstein system. Via the linear stability analysis we determine both the Turing and the Hopf instability boundaries and we show how nonlinear ...
Gambino, G. +2 more
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Turing Instability and Spatial Pattern Formation in a Model of Urban Crime
MathematicsA nonlinear crime model is generalized by introducing self- and cross-diffusion terms. The effect of diffusion on the stability of non-negative constant steady states is applied.
Isabella Torcicollo, Maria Vitiello
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Reaction-diffusion models for biological pattern formation [PDF]
, 2001 We consider the use of reaction-diffusion equations to model biological pattern formation and describe the derivation of the reaction-terms for several illustrative examples.
Crampin, E. J., Maini, P. K.
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Advances in Difference Equations, 2018 We study the pattern generating mechanism of a generalized Gierer–Meinhardt model with diffusions. We show the existence and stability of the Hopf bifurcation for the corresponding kinetic system under certain conditions.
Jinliang Wang, You Li, Xiaojie Hou
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Advanced Materials, EarlyView.A green, freeform manufacturing approach that utilizes robust aqueous two‐phase systems to create intricate and scalable photonic structures and non‐planar mechanochromic hydrogel actuators from plant‐based hydroxypropyl cellulose. This approach broadens the structural possibilities of sustainable photonic devices and mechanochromic systems, offering ...
Xiao Song +14 more
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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.
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Pattern Formation in Non‐Equilibrium Architected Materials
Advanced Materials Technologies, EarlyView.This article demonstrates an artificial mechanical system ‐ a robotic metamaterial ‐ as an accessible and versatile platform within which to explore and prescribe the reaction‐diffusion driven pattern formation hitherto associated with comparatively less accessible and versatile non‐equilibrium biological and chemical systems.
Vinod Ramakrishnan, Michael J. Frazier
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Pattern Formation in a Semi-Ratio-Dependent Predator-Prey System with Diffusion
Discrete Dynamics in Nature and Society, 2013 We investigate spatiotemporal dynamics of a semi-ratio-dependent predator-prey system with reaction-diffusion and zero-flux boundary. We obtain the conditions for Hopf, Turing, and wave bifurcations of the system in a spatial domain by making use of the ...
Hunki Baek, Dong Ick Jung, Zhi-wen Wang
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The Diffusion-Driven Instability for a General Time-Space Discrete Host-Parasitoid Model
Discrete Dynamics in Nature and Society, 2023 In this paper, we consider a general time-space discrete host-parasitoid model with the periodic boundary conditions. We analyzed and obtained some usual conditions, such as Turing instability occurrence, Flip bifurcation occurrence, and Neimark-Sacker ...
Xuetian Zhang, Chunrui Zhang
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