Regulatory dynamics in systems biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the distinction between stable and unstable dynamics is usually made by checking damage after flip perturbations . Here we point out that this notion of stability is incompatible with the stability properties of the original continuous dynamics probed by small perturbations . In particular, random networks of nodes with large sensitivity yield stable dynamics , in contrast to the prediction of chaos obtained by flip perturbationsin Boolean networks .
Regulatory dynamics in biology is often described by continuous rate equations for continuously varying chemical concentrations. Binary discretization of state space and time leads to Boolean dynamics. In the latter, the dynamics has been called unstable if flip perturbations lead to damage spreading . Here we find that this stability classification strongly differs from the stability properties of the original continuous dynamics under small perturbations of the state vector . In particular, random networks of nodes with large sensitivity yield stable dynamics under small perturbations .
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systems
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distinction between stable and unstable dynamics is usually made by checking damage after flip perturbations
dynamics has been called unstable if flip perturbations lead to damage spreading
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point out that this notion of stability is incompatible with
find that this stability classification strongly differs from
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probed by small perturbations
under small perturbations of the state vector
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, in contrast to the prediction of chaos obtained by flip perturbationsin Boolean networks
under small perturbations