Logistic functions serve as a robust replacement for Hill functions in GRN modeling by eliminating analytical pathologies for non-integer coefficients while preserving threshold sensitivity and enabling explicit well-posedness proofs.
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Logistic reformulations of delay-coupled gene regulatory networks are globally smooth and positive at zero, with matched parameters, unique equilibria, Hopf bifurcation at critical delays, and substantially smaller Lipschitz constants than Hill-based versions.
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Exploring Logistic Functions as Robust Alternatives to Hill Functions in Genetic Network Modeling
Logistic functions serve as a robust replacement for Hill functions in GRN modeling by eliminating analytical pathologies for non-integer coefficients while preserving threshold sensitivity and enabling explicit well-posedness proofs.
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Beyond Linear Additive and Hill Functions: A General Logistic Reformulation of Delay-Coupled Gene Regulatory Networks with Equilibrium Analysis, Hopf Bifurcation, and Lipschitz Stability
Logistic reformulations of delay-coupled gene regulatory networks are globally smooth and positive at zero, with matched parameters, unique equilibria, Hopf bifurcation at critical delays, and substantially smaller Lipschitz constants than Hill-based versions.