Displaying similar documents to “The resonance phenomenon in the reaction-diffusion systems.”

Atherosclerosis Initiation Modeled as an Inflammatory Process

N. El Khatib, S. Génieys, V. Volpert (2010)

Mathematical Modelling of Natural Phenomena

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In this work we study the inflammatory process resulting in the development of atherosclerosis. We develop a one- and two-dimensional models based on reaction-diffusion systems to describe the set up of a chronic inflammatory response in the intima of an artery vessel wall. The concentration of the oxidized low density lipoproteins (ox-LDL) in the intima is the critical parameter of the model. Low ox-LDL concentrations do not lead to a chronic inflammatory reaction. Intermediate ox-LDL...

Dynamics of Propagation Phenomena in Biological Pattern Formation

G. Liţcanu, J. J.L. Velázquez (2010)

Mathematical Modelling of Natural Phenomena

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A large variety of complex spatio-temporal patterns emerge from the processes occurring in biological systems, one of them being the result of propagating phenomena. This wave-like structures can be modelled via reaction-diffusion equations. If a solution of a reaction-diffusion equation represents a travelling wave, the shape of the solution will be the same at all time and the speed of propagation of this shape will be a constant. Travelling wave solutions of reaction-diffusion systems...