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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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Global Coupling of an Interface Problem in an Activator-inhibitor System
Journal of Partial Differential Equations, 2003This work is devoted to the study of the existence of periodic solutions and bifurcation of the interface problem for the case of global coupling and the case of a strong coupling. The author proves the theorem of the existence of solutions and finds the stationary solutions.
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Control of activator-inhibitor systems by differential transport
Physics Letters A, 1996Abstract When an activator-inhibitor system switches from a spatially uniform to a patterned state by a differential transport instability — the differential flow instability, or the diffusive or Turing instability — the values of variables, such as concentrations or reaction rates, including their averages, may drastically change.
Arkady B Rovinsky +3 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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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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Stability of least energy patterns of the shadow system for an activator-inhibitor model
Japan Journal of Industrial and Applied Mathematics, 2001zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Ni, Wei-Ming +2 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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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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[The role of cathepsins and the plasminogen activator/inhibitor system in colorectal cancer].
Orvosi hetilap, 1999Cysteine proteases [Cathepsin B and L (CATB, CATL)] and the serine protease urokinase type plasminogen activator (UPA) with its inhibitor type-1 (PAI-1) are thought to play an important part in colorectal cancer invasion and metastasis. To our knowledge, however, cathepsins and plasminogen activator/inhibitor system have not been evaluated in the same ...
Herszényi L +8 more
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