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Distribution-dependent stochastic dynamical systems arise widely inengineering and science. We consider a class of such systems which model thelimit behaviors of interacting particles moving in a vector field with randomfluctuations. We aim to examine the most likely transition path betweenequilibrium stable states of the vector field. In the small noise regime, theaction functional does not involve the solution of the skeleton equation whichdescribes the unperturbed deterministic flow of the vector field shifted by theinteraction at zero distance. As a result, we are led to study the most likelytransition path for a stochastic differential equation without distributiondependency. This enables the computation of the most likely transition path forthese distribution-dependent stochastic dynamical systems by the adaptiveminimum action method and we illustrate our approach in two examples.

The Most Likely Transition Path for a Class of Distribution-Dependent Stochastic Systems