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Existence of solution for a class of activator–inhibitor systems
Glasgow Mathematical Journal, 2022AbstractWe 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, 2012zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Datsko, B., Gafiychuk, V.
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Feedback loops for chaos in activator-inhibitor systems
The Journal of Chemical Physics, 2005Previous 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, 2005Activator-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 +2 more
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Hopf bifurcation in an activator–inhibitor system with network
Applied Mathematics Letters, 2019zbMATH Open Web Interface contents unavailable due to conflicting licenses.
Yanling Shi, Zuhan Liu, Canrong Tian
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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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Stable Patterns Generated by Activator-Inhibitor Systems
Mathematical Medicine and Biology, 1986The 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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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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