Turbulence near cyclic fold bifurcations in birhythmic media

Details Turbulence near cyclic fold bifurcations in birhythmic media Turbulence near cyclic fold bifurcations in birhythmic media

2004-02-24

arxiv.org/abs/q-bio/0402040v1

Biology

Quantitative Biology

Subcellular Processes

14 pages 10 figures

Scientific paper

10.1103/PhysRevE.70.026212

We show that at the onset of a cyclic fold bifurcation, a birhythmic medium composed of glycolytic oscillators displays turbulent dynamics. By computing the largest Lyapunov exponent, the spatial correlation function, and the average transient lifetime, we classify it as a weak turbulence with transient nature. Virtual heterogeneities generating unstable fast oscillations are the mechanism of the transient turbulence. In the presence of wavenumber instability, unstable oscillations can be reinjected leading to stationary turbulence. We also find similar turbulence in a cell cycle model. These findings suggest that weak turbulence may be universal in biochemical birhythmic media exhibiting cyclic fold bifurcations.

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