Results 51 to 60 of about 8,750 (185)
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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Entropy, 2017 The formation of self-organized patterns in predator-prey models has been a very hot topic recently. The dynamics of these models, bifurcations and pattern formations are so complex that studies are urgently needed.
Feifan Zhang +5 more
doaj +1 more source
Cross-Diffusion-Driven Instability in a Predator-Prey System with Fear and Group Defense
Mathematics, 2020 In this paper, a reaction-diffusion prey-predator system including the fear effect of predator on prey population and group defense has been considered.
Maria Francesca Carfora +1 more
doaj +1 more source
Nonlinear Analysis, 2021 In this paper, we consider the dynamics of delayed Gierer–Meinhardt system, which is used as a classic example to explain the mechanism of pattern formation. The conditions for the occurrence of Turing, Hopf and Turing–Hopf bifurcation are established by
Shuangrui Zhao +2 more
doaj +1 more source
Traveling and pinned fronts in bistable reaction-diffusion systems on network [PDF]
, 2012 Traveling fronts and stationary localized patterns in bistable reaction-diffusion systems have been broadly studied for classical continuous media and regular lattices. Analogs of such non-equilibrium patterns are also possible in networks.
Alexander S. Mikhailov +3 more
core +4 more sources
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
doaj +1 more source
Pattern formation in spatially heterogeneous Turing reaction-diffusion models [PDF]
, 2003 The Turing reaction–diffusion model [Phil. Trans. R. Soc. 237 (1952) 37–72] for self-organised spatial pattern formation has been the subject of a great deal of study for the case of spatially homogeneous parameters.
Maini, P. K., Monk, N. A. M., Page, K.
core +2 more sources
Study on the Compatibility of Multi-Bifurcations by Simulations of Pattern Formation
IEEE Access, 2019 Bifurcation is considered the main mathematical mechanism for the formation of spatial self-organizing patterns in many studies. When bifurcation was initially defined, only the transition of the system from stable state to unstable state or from uniform
Feifan Zhang +4 more
doaj +1 more source
Spatiotemporal complexity of a ratio-dependent predator-prey system
, 2007 In this paper, we investigate the emergence of a ratio-dependent predator-prey system with Michaelis-Menten-type functional response and reaction-diffusion. We derive the conditions for Hopf, Turing and Wave bifurcation on a spatial domain.
A. M. Turing +12 more
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Vegetation patterns pinpoint the least resilient dryland sites
Methods in Ecology and Evolution, Volume 17, Issue 1, Page 172-187, January 2026.Abstract Resource‐limited ecosystems, such as drylands, can exhibit self‐organized spatial patterns. Theory suggests that changes in these patterns can inform about the ecosystem degradation level. While the current theory is expected to work well when following a given site in time, we still lack ways of comparing different field sites using static ...
Benoît Pichon +3 more
wiley +1 more source