Results 31 to 40 of about 970 (177)
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
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Cell-Size Confinement Drives Size-Dependent Scaling of Intracellular Reaction-Diffusion Waves for Robust Patterning. [PDF]
Small SciIntracellular reaction‐diffusion (iRD) waves scale their wavelength to space size when they are confined within cell‐size spaces, despite having intrinsic wavelength in open systems. This wavelength selection ensures the scaling of the wave shape and the velocity, preserving these essential properties against physicochemical perturbations. This scaling
Takada S +5 more
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Mathematical Models and Methods in Applied SciencesFollowing the approach pioneered by Eckhaus, Mielke, Schneider, and others for reaction–diffusion systems, we justify rigorously by Lyapunov–Schmidt reduction the formal amplitude (complex Ginzburg–Landau) equations describing Turing-type bifurcations of general reaction–diffusion–convection systems, showing that small spatially periodic traveling wave
Aric Wheeler, Kevin Zumbrun
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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
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Pattern Dynamics in a Predator-Prey Model with Diffusion Network
Complexity, 2022 Diffusion plays an essential role in the distribution of predator and prey. We mainly research the diffusion network’s effect on the predator-prey model through bifurcation.
Wenjie Yang +3 more
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Hopf Bifurcation Analysis of a Diffusive Nutrient–Phytoplankton Model with Time Delay
Axioms, 2022 In this paper, we studied a nutrient–phytoplankton model with time delay and diffusion term. We studied the Turing instability, local stability, and the existence of Hopf bifurcation.
Ruizhi Yang, Liye Wang, Dan Jin
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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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Investigation of Turing structures formation under the influence of wave instability [PDF]
Компьютерные исследования и моделирование, 2019 A classical for nonlinear dynamics model, Brusselator, is considered, being augmented by addition of a third variable, which plays the role of a fast-diffusing inhibitor.
Maxim Borisovich Kuznetsov
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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
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Steady-state bifurcation of FHN-type oscillator on a square domain
Nonlinear Analysis, 2023 The Turing patterns of reaction-diffusion equations defined over a square region are more complex because of the D4-symmetry of the spatial region. This leads to the occurrence of multiple equivariant Turing bifurcations.
Chunrui Zhang +2 more
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