Limit cycles and detailed balance in Fokker-Planck equations

A class of non-linear Fokker Planck equations with exactly known steady state solution is investigated and its relation with the models considered earlier in the literature is discussed. A characterisation of the absence of detailed balance and possible existence of limit cycles is given. The implications of detailed balance on the existence and the character of limit cycle behaviour are studied. It is shown that detailed balance does not determine the existence or non-existence of limit cycles but rather their character.