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Abstract: Linearized catalytic reaction equations modeling e.g. the dynamics of geneticregulatory networks under the constraint that expression levels, i.e. molecularconcentrations of nucleic material are positive, exhibit nontrivial dynamicalproperties, which depend on the average connectivity of the reaction network.In these systems the inflation of the edge of chaos and multi-stability havebeen demonstrated to exist. The positivity constraint introduces a nonlinearitywhich makes chaotic dynamics possible. Despite the simplicity of such minimallynonlinear systems, their basic properties allow to understand fundamentaldynamical properties of complex biological reaction networks. We analyze theLyapunov spectrum, determine the probability to find stationary oscillatingsolutions, demonstrate the effect of the nonlinearity on the effective in- andout-degree of the active interaction network and study how the frequencydistributions of oscillatory modes of such system depend on the averageconnectivity.



Author: Rudolf Hanel, Manfred Pöchacker, Stefan Thurner

Source: https://arxiv.org/







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