Abstract
The behaviour of similar coupled non-linear oscillators of the type \(\dot x\)=f(x, y, µ \(\dot y\)=g(x, y, µ is to be investigated. The oscillators are assumed to be coupled by diffusion gradients. If some conditions on the magnitude of the diffusion coefficients are satisfied, it is proved that: 1) if the oscillators have the same period (identical value of the parameter μ) and different phases before coupling, after coupling they tend to synchronize the phases; 2) if the periods of the oscillators are not too different (in terms of the values of the parameter μ) before coupling, after coupling they tend to oscillate with the same period. It is suggested the possible role of diffusion as a synchronizing mechanism in some biological phenomena.
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Torre, V. Synchronization of non-linear biochemical oscillators coupled by diffusion. Biol. Cybernetics 17, 137–144 (1975). https://doi.org/10.1007/BF00364162
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DOI: https://doi.org/10.1007/BF00364162