In a network of interconnected biochemical reactants, after each reactions the mass concentrations of the reactants change, governed by some rules. Each reactions may be described either as deterministic or as stochastic. This depends on the mass concentration of the involved reactants. If the mass is high, then a deterministic modelization is good; if the mass is low, then a stochastic modelization is better. A "deterministic modelization" means "by an ordinary differential equation, in continuous time"; a "stochastic modelization" means "by a sequence of random instants at which the reaction occurs". Deterministic or stochastic, the mass of the reactants changes anyway, and reactions that were described as deterministic may become stochastic and vice-versa. The idea for the thesis is to write down this kind of hybrid deterministic/stochastic system and to study some of its properties, for examples: uniqueness of the solutions, dependence on the initial states, asymptotic behaviour for long time.... Some numerical simulations may be also treated.
Notions about the theory of ordinary differential equations and about stochastic processes are of course welcome. Some support by a possible co-supervisor from systems biology may be provided.