4 papers
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…
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…
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…
Computer-aided analysis of high-dimensional Glass networks: periodicity, chaos, and bifurcations in a ring circuit
Ismail Belgacem, Roderick Edwards, Etienne Farcot
Glass networks model systems of variables that interact via sharp switching. A body of theory has been developed over several decades that, in principle, allows rigorous proof of d…