Differential automata and their discrete simulators
Non-Linear Analysis
Parallel simulated annealing by mixing of states
Journal of Computational Physics
Qualitative Theory of Hybrid Dynamical Systems
Qualitative Theory of Hybrid Dynamical Systems
Accurate hybridization of nonlinear systems
Proceedings of the 13th ACM international conference on Hybrid systems: computation and control
Modular rate laws for enzymatic reactions
Bioinformatics
Tropical Geometries and Dynamics of Biochemical Networks Application to Hybrid Cell Cycle Models
Electronic Notes in Theoretical Computer Science (ENTCS)
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We discuss piecewise smooth hybrid systems as models for regulatory networks in molecular biology. These systems involve both continuous and discrete variables. The discrete variables allow to switch on and off some of the molecular interactions in the model of the biological system. Piecewise smooth hybrid models are well adapted to approximate the dynamics of multiscale dissipative systems that occur in molecular biology. We show how to produce such models by a top down approach that use biological knowledge for a guided choice of important variables and interactions. Then we propose an algorithm for fitting parameters of the piecewise smooth models from data. We illustrate some of the possibilities of this approach by proposing hybrid versions of eukaryotic cell cycle regulation.