Dynamical Stability after Perturbation in a Discontinuous Coupled Map Lattice

In this paper we show that coupled map lattice (CML) formalisms can be applied to study some general features of biological systems from a molecular point of view. In particular, we analyze the stability of such systems with respect to perturbations. Specifically we show that the response of the model, of coupled formal genetic networks, to finite amplitude perturbations may strongly depend on the level of the spatial coupling, which determines different dynamical transient regimes before a periodic evolution is eventually attained. In particular we observe transients that grow exponentially with the system size, while the exact computation of the spectrum of the Lyapunov exponents indicates that the maximum is always negative, independent of the coupling strength. A complete characterization of the correspondence between stability properties and dynamical features of the model has been obtained by extended dynamical simulations. An interpretation of these results in a biological perspective indicates that signal transduction should be considered as a possible mechanism of modification of gene expression by transient perturbations on cell populations.