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Hopf bifurcation and Turing instability in a diffusive predator-prey model with hunting cooperation
Open Mathematics, 2022 In this article, we study Hopf bifurcation and Turing instability of a diffusive predator-prey model with hunting cooperation. For the local model, we analyze the stability of the equilibrium and derive conditions for determining the direction of Hopf ...
Miao Liangying, He Zhiqian
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Differential susceptibility to noise of mixed Turing and Hopf modes in a photosensitive chemical medium [PDF]
, 2007 We report on experiments with the photosensitive chlorine dioxide-iodine-malonic acid reaction (CDIMA) when forced with a random (spatiotemporally) distributed illumination. Acting on a mixed mode consisting of oscillating spots, close enough to the Hopf
Alonso Muñoz, Sergio +2 more
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Turing-Hopf bifurcation analysis in a diffusive Gierer-Meinhardt model
AIMS Mathematics, 2021 The reaction-diffusion Gierer-Meinhardt system in one dimensional bounded domain is considered in the present paper. The Hopf bifurcation is investigated, which is found to be degenerate.
Anna Sun, Ranchao Wu, Mengxin Chen
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Bifurcation Analysis of a Generic Reaction–Diffusion Turing Model [PDF]
International Journal of Bifurcation and Chaos, 2014 A generic Turing type reaction–diffusion system derived from the Taylor expansion near a constant equilibrium is analyzed. The existence of Hopf bifurcations and steady state bifurcations is obtained. The bifurcation direction and the stability of the bifurcating periodic obits are calculated.
Liu, Ping +3 more
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Allee effect-driven complexity in a spatiotemporal predator-prey system with fear factor
Mathematical Biosciences and Engineering, 2023 In this paper, we propose a spatiotemporal prey-predator model with fear and Allee effects. We first establish the global existence of solution in time and provide some sufficient conditions for the existence of non-negative spatially homogeneous ...
Yuhong Huo +4 more
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Additive Global Noise Delays Turing Bifurcations
Physical Review Letters, 2007 We apply a stochastic center manifold method to the calculation of noise-induced phase transitions in the stochastic Swift-Hohenberg equation. This analysis is applied to the reduced mode equations that result from Fourier decomposition of the field variable and of the temporal noise. The method shows a pitchfork bifurcation at lower perturbation order,
Hutt, Axel +2 more
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Non-linear effects on Turing patterns: time oscillations and chaos. [PDF]
, 2012 We show that a model reaction-diffusion system with two species in a monostable regime and over a large region of parameter space, produces Turing patterns coexisting with a limit cycle which cannot be discerned from the linear analysis. As a consequence,
Aragón, J. L. +4 more
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Spatiotemporal dynamics and Turing patterns in an eco-epidemiological model with cannibalism
Results in Control and Optimization, 2022 In this work, we have studied the spatiotemporal dynamics and pattern formation in an eco-epidemiological model with cannibalism, which are not explored in the existing literature.
Vikas Kumar +2 more
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Labyrinthine Turing Pattern Formation in the Cerebral Cortex [PDF]
, 2002 I propose that the labyrinthine patterns of the cortices of mammalian brains may be formed by a Turing instability of interacting axonal guidance species acting together with the mechanical strain imposed by the interconnecting axons.Comment: See home ...
BAIER +41 more
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Boundary Value Problems, 2017 Spatiotemporal patterns driven by cross-diffusion of a uni-directional consumer-resource (C-R) system with Holling-II type functional response are investigated in this paper.
Renji Han, Binxiang Dai
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