Dynamics of self-replicating patterns in reaction diffusion systems
- 25 April 1994
- journal article
- research article
- Published by American Physical Society (APS) in Physical Review Letters
- Vol. 72 (17), 2797-2800
- https://doi.org/10.1103/physrevlett.72.2797
Abstract
Recently solutions to a simple reaction diffusion system have been discovered in which localized structures (spots) make copies of themselves. In this Letter we analyze the one-dimensional analog of this process in which replication occurs until the domain is filled with a periodic array of spots. We provide a heuristic explanation of why this replication process should occur in a broad class of systems. Time dependent solutions are developed for model systems and their analytic structures investigated.Keywords
This publication has 9 references indexed in Scilit:
- Complex Patterns in a Simple SystemScience, 1993
- Pattern Formation by Interacting Chemical FrontsScience, 1993
- Self-organization in active distributed media: scenarios for the spontaneous formation and evolution of dissipative structuresSoviet Physics Uspekhi, 1990
- Pattern sensitivity to boundary and initial conditions in reaction-diffusion modelsJournal of Mathematical Biology, 1986
- Autocatalytic reactions in the isothermal, continuous stirred tank reactorChemical Engineering Science, 1983
- Dissipative structures and morphogenetic pattern in unicellular algaePhilosophical Transactions of the Royal Society of London. B, Biological Sciences, 1981
- Self‐Oscillations in Glycolysis 1. A Simple Kinetic ModelEuropean Journal of Biochemistry, 1968
- On the Occurrence of Oscillations around the Steady State in Systems of Chemical Reactions far from EquilibriumThe Journal of Chemical Physics, 1967