A nonlinear two-species oscillatory system: bifurcation and stability analysis.
Bandyopadhyay, Malay, Bhattacharya, Rakhi, Chakrabarti, C.G. (2003)
International Journal of Mathematics and Mathematical Sciences
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Bandyopadhyay, Malay, Bhattacharya, Rakhi, Chakrabarti, C.G. (2003)
International Journal of Mathematics and Mathematical Sciences
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Shu Dai, David G. Schaeffer (2010)
ESAIM: Mathematical Modelling and Numerical Analysis
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While alternans in a single cardiac cell appears through a simple period-doubling bifurcation, in extended tissue the exact nature of the bifurcation is unclear. In particular, the phase of alternans can exhibit wave-like spatial dependence, either stationary or travelling, which is known as alternans. We study these phenomena in simple cardiac models through a modulation equation proposed by Echebarria-Karma. As shown in our previous paper, the zero solution of their equation may...
Meron, Ehud (1999)
Discrete Dynamics in Nature and Society
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P.M.J. Trevelyan, A. Pereira, S. Kalliadasis (2012)
Mathematical Modelling of Natural Phenomena
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Consider the dynamics of a thin film flowing down an inclined plane under the action of gravity and in the presence of a first-order exothermic chemical reaction. The heat released by the reaction induces a thermocapillary Marangoni instability on the film surface while the film evolution affects the reaction by influencing heat/mass transport through convection. The main parameter characterizing the reaction-diffusion process is the Damköhler number. We investigate the complete range...
Jan Eisner (2000)
Mathematica Bohemica
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Sufficient conditions for destabilizing effects of certain unilateral boundary conditions and for the existence of bifurcation points for spatial patterns to reaction-diffusion systems of the activator-inhibitor type are proved. The conditions are related with the mollification method employed to overcome difficulties connected with empty interiors of appropriate convex cones.
Jan Eisner, Milan Kučera (1997)
Applications of Mathematics
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We consider a reaction-diffusion system of the activator-inhibitor type with boundary conditions given by inclusions. We show that there exists a bifurcation point at which stationary but spatially nonconstant solutions (spatial patterns) bifurcate from the branch of trivial solutions. This bifurcation point lies in the domain of stability of the trivial solution to the same system with Dirichlet and Neumann boundary conditions, where a bifurcation of this classical problem is excluded. ...