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math.DS2026
Logistic Gene Regulatory Networks: A Modelling Framework Beyond Hill Functions
Ismail Belgacem
Boolean networks model gene regulatory networks, but extracting quantitative dynamics requires translating their logical rules into differential equations, and the sigmoidal kernel…
math.DS2026
State-Feedback Control of Logistic-Based Gene Regulatory Networks: Closed-Form Lyapunov Certificates, Monostabilization, and Delay-Uniform Stability
Ismail Belgacem
Gene regulatory networks (GRNs) are high-value targets for therapeutic and synthetic-biology control. Classical Hill models carry a structural defect: the production term vanishes…
math.DS2026
Sustained Limit Cycles in the Logistic Two-Gene Genetic Oscillator: A Delay-Driven Hopf Bifurcation
Ismail Belgacem
The logistic two-gene negative-feedback oscillator is locally asymptotically stable for all biological parameter values, since the trace of the Jacobian is uniformly negative. Real…