Chaos in a bienzymatic cyclic model with two autocatalytic loops |
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Authors: | H Berry |
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Institution: | Equipe de Recherche sur les Relations Matrice Extracellulaire-Cellules (ERRMECe), Université de Cergy-Pontoise, 2 avenue A. Chauvin. B.P. 222, Cergy Pontoise Cedex 95302, France |
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Abstract: | A general bienzymatic cyclic system including two autocatalytic loops is studied and used as a basic design principle for modelling extracellular matrix turnover. Using classical enzyme kinetic rates, the model is described by a set of four ordinary differential equations and numerically studied by bifurcation diagrams and Poincaré sections. We observe limit-cycle oscillations and chaotic behaviors arising from period-doubling cascades or intermittency. Chaotic oscillations originate from distinct strange attractors that undergo boundary and internal crisis. For some parameter values, the system presents several bistable areas, where a limit cycle coexists with another one or with a strange attractor. The dynamics are qualitatively modified when the weight of the autocatalytic loops on the system varies, resulting in the change in the number of attractors. |
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