Delay-differential extension of the logistic two-gene oscillator undergoes a Hopf bifurcation at explicit critical total delay τ_c with closed-form ω_c, transversality bound, and supercritical amplitude laws, matching p53 data within 3%.
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Logistic functions replace Hill functions in gene regulatory network ODE models to ensure global smoothness, real-valued trajectories, positive basal production, and stable numerical integration across small and large networks.
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.
citing papers explorer
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Sustained Limit Cycles in the Logistic Two-Gene Genetic Oscillator: A Delay-Driven Hopf Bifurcation
Delay-differential extension of the logistic two-gene oscillator undergoes a Hopf bifurcation at explicit critical total delay τ_c with closed-form ω_c, transversality bound, and supercritical amplitude laws, matching p53 data within 3%.
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Logistic Gene Regulatory Networks: Prevention of Expression Shutdown, and Numerical Stability Beyond Hill Function
Logistic functions replace Hill functions in gene regulatory network ODE models to ensure global smoothness, real-valued trajectories, positive basal production, and stable numerical integration across small and large networks.
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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.