Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the limiting behaviour of stochastic models of populations of interacting agents, as the number of agents goes to infinity. Classical mean-field results have established that this limiting behaviour is described by an ordinary differential equation ODE under two conditions: 1 that the dynamics is smooth; and 2 that the population is composed of a finite number of homogeneous sub-populations, each containing a large number of agents.  reviews recent work showing what happens if these conditions do not hold. In these cases, it is still possible to exhibit a limiting regime at the price of replacing the ODE by a more complex dynamical system. In the case of non-smooth or uncertain dynamics, the limiting regime is given by a differential inclusion. In the case of multiple population scales, the ODE is replaced by a stochastic hybrid automaton.
['Luca Bortolussi', 'Nicolas Gast']
I am writing a research paper on a idea Mean-Field Limits Beyond Ordinary Differential Equations
[{"from": "human", "value": "I am writing a research paper on a idea Mean-Field Limits Beyond Ordinary Differential Equations"}, {"from": "gpt", "value": "Thats a unique idea.You should consider the following idea to enhance your idea so that it would impact uniquely:  study the limiting behaviour of stochastic models of populations of interacting agents, as the number of agents goes to infinity. Classical mean-field results have established that this limiting behaviour is described by an ordinary differential equation ODE under two conditions: 1 that the dynamics is smooth; and 2 that the population is composed of a finite number of homogeneous sub-populations, each containing a large number of agents.  reviews recent work showing what happens if these conditions do not hold. In these cases, it is still possible to exhibit a limiting regime at the price of replacing the ODE by a more complex dynamical system. In the case of non-smooth or uncertain dynamics, the limiting regime is given by a differential inclusion. In the case of multiple population scales, the ODE is replaced by a stochastic hybrid automaton."}]