Hyperchaos and chemical turbulence in enzymatic reaction-diffusion systems

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Abstract
We derive two kinetic models based on commonly occurring, simple enzymatic reactions. The first belongs to the class of activator-inhibitor models, whereas the second is a Selkov-type substrate-depletion model. The bifurcation behavior of both models is studied in a spatially homogeneous environment. We consider one-dimensional arrays of N oscillatory reaction cells coupled by diffusion. For small N we find two kinds of hyperchaos depending on a bifurcation parameter and the ratio of the diffusion coefficients of activator and inhibitor (Da/Di). For large N and Da/Di≳1, we observe spatiotemporally chaotic states characterized by phase defects. For Da/Di<1, we find a chemical turbulent state emerging from the interaction of a Hopf and a Turing instability in both models.

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