Meeting of Chemical Wave Fronts Creates Chaos

Sergey Vakulenko () and Alexander Galper
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Sergey Vakulenko: Institute for Problems in Mechanical Engineering RAS., Bolshoy pr. V.O. 61, 199178 Saint Petersburg, Russia
Alexander Galper: Independent Researcher, 199178 Saint Petersburg, Russia

Mathematics, 2024, vol. 12, issue 3, 1-16

Abstract: We consider systems of reaction–diffusion equations. We describe a new effect in the wave interaction for these systems: the collision of several travelling fronts may induce chaos or periodic oscillations. This effect depends on the initial locations of the travelling fronts: For some initial positions chaos occurs and for others it does not. In a space-homogeneous system, we need at least three fronts to create time-periodic behaviour, while to create chaos, we should have four fronts. We also provide a short review of previously known results, and different known mechanisms of chaos generation for reaction–diffusion systems. Our results can be used for pattern coding, in particular, for morphogenesis.

Keywords: reaction–diffusion systems; waves; chaos (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2024
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