Results 291 to 300 of about 338,751 (320)

Existence of solution for a class of activator–inhibitor systems

Glasgow Mathematical Journal, 2022
AbstractWe prove the existence of a solution for a class of activator–inhibitor system of type $- \Delta u +u = f(u) -v$ , $-\Delta v+ v=u$ in $\mathbb{R}^{N}$ . The function f is a general nonlinearity which can grow polynomially in dimension $N\geq 3$ or exponentiallly if $N=2$ . We are able to treat f when it has critical growth corresponding
Giovany Figueiredo, Marcelo Montenegro
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Complex nonlinear dynamics in subdiffusive activator–inhibitor systems

Communications in Nonlinear Science and Numerical Simulation, 2012
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Datsko, B., Gafiychuk, V.
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Feedback loops for chaos in activator-inhibitor systems

The Journal of Chemical Physics, 2005
Previous investigations have revealed that special constellations of feedback loops in a network can give rise to saddle-node and Hopf bifurcations and can induce particular bifurcation diagrams including the occurrence of various codimension-two points.
Sensse, A., Eiswirth, M.
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Turing pattern formation in fractional activator-inhibitor systems

Physical Review E, 2005
Activator-inhibitor systems of reaction-diffusion equations have been used to describe pattern formation in numerous applications in biology, chemistry, and physics. The rate of diffusion in these applications is manifest in the single parameter of the diffusion constant, and stationary Turing patterns occur above a critical value of d representing the
B I, Henry, T A M, Langlands, S L, Wearne   +2 more
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Hopf bifurcation in an activator–inhibitor system with network

Applied Mathematics Letters, 2019
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Yanling Shi, Zuhan Liu, Canrong Tian
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Control of activator-inhibitor systems by differential transport

Physics Letters A, 1996
Abstract 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, Satoshi Nakata, Vladimir Z Yakhnin, Michael Menzinger   +3 more
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Stable Patterns Generated by Activator-Inhibitor Systems

Mathematical Medicine and Biology, 1986
The paper is concerned with a discrete morphogenetic model of activator-inhibitor type. The aim is to give a theoretical explanation for what we understand as the first step in pattern formation for a growing object: as long as the object remains small enough, its shape is spatially homogeneous, while passing a critical length results in a spontaneous ...
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