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Turing pattern dynamics in an activator-inhibitor system with superdiffusion
Physical Review E, 2014The fractional operator is introduced to an activator-inhibitor system to describe species anomalous superdiffusion. The effects of the superdiffusive exponent on pattern formation and pattern selection are studied. Our linear stability analysis shows that the wave number of the Turing pattern increases with the superdiffusive exponent.
Lai, Zhang, Canrong, Tian
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Diffusive instabilities in a hyperbolic activator-inhibitor system with superdiffusion
Physical Review E, 2018We investigate analytically and numerically the conditions for wave instabilities in a hyperbolic activator-inhibitor system with species undergoing anomalous superdiffusion. In the present work, anomalous superdiffusion is modeled using the two-dimensional Weyl fractional operator, with derivative orders α∈ [1,2].
Alain, Mvogo +2 more
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Application of the activator inhibitor principle to physical systems
Physics Letters A, 1989Abstract The transition from a spatially homogeneous state into a spatially periodic state and the development of solitary filaments are observed experimentally in an electrical network and in a dc-gas discharge system, respectively. The explanation for these phenomena is done in terms of the biomathematical activator inhibitor principle with the ...
H.-G. Purwins +5 more
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Degenerate Turing Bifurcation and the Birth of Localized Patterns in Activator-Inhibitor Systems
SIAM Journal on Applied Dynamical Systems, 2023zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Edgardo Villar-Sepúlveda +1 more
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On modelling pattern formation by activator-inhibitor systems
Journal of Mathematical Biology, 1977The formation of spatially patterned structures in biological organisms has been modelled in recent years by various mechanisms, including pairs of reaction-diffusion equations $$u_t = D_{\text{1}} \nabla ^{\text{2}} u + f(u,v)$$ , $$v_t = D_{\text{2}} \nabla ^{\text{2}} v + g(u,v)$$ .
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Decaying localized structures beyond Turing space in an activator–inhibitor system
The European Physical Journal Plus, 2020We perform numerical simulations beyond Turing space in an activator–inhibitor system involving quadratic and cubic nonlinearities . We show that while all the three fixed points of the system are stable nodes, it exhibits spatially stable patterns as diverse as labyrinths, worms, negatons, and combination of them.
Dhritiman Talukdar, Kishore Dutta
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Fibrinolytic system of cultured endothelial cells: Regulation by plasminogen activator inhibitor
Journal of Cellular Biochemistry, 1986AbstractCultured bovine aortic endothelial cells have a relatively complex flbrinolytic system that is responsive to both the physiological state of the cell itself and to a variety of agents added to the culture medium. The flbrinolytic activity of these cells results from the production of both urokinase‐type and tissue‐type plasminogen activators ...
D J, Loskutoff +3 more
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Asymptotic Solution of Activator Inhibitor Systems for Nonlinear Reaction Diffusion Equations
Journal of Systems Science and Complexity, 2008zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Mo, Jiaqi, Lin, Wantao
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Propagation of fronts in activator-inhibitor systems with a cutoff
The European Physical Journal B, 2005We consider a two-component system of reaction-diffusion equations with a small cutoff in the reaction term. A semi-analytical solution of fronts and how the front velocities vary with the parameters are given for the case when the system has a piecewise linear nonlinearity.
E. P. Zemskov, V. Méndez
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No Oscillations in Real Activator–Inhibitor Systems in Accomplishing Pattern Formation
Bulletin of Mathematical Biology, 2012In contrast to the claims put forward in several recent papers in this journal, for the known activator–inhibitor systems for pattern formation there is no risk to enter into an oscillating mode. In these systems, the inhibition takes place outside of the cells by blocking the receptors that are involved in the self-enhancing reaction. Therefore, there
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