A note on the Melnikov function - Dinh, Nguyen Van (Vietnam Journal of Mechanics, 2007)
With one (Poincaré section) parameter and a particular motion law (that associated to certain determined point of horno-heteroclinic orbits), the usual form of the Melnikov function seems to be not convenient for certain problems. Another favorable form can be obtained by using a supplementary parameter - the arbitrary time constant in the general mentioned motion law