Your calls are made recursively which pushes functions on to the stack infinitely that causes max call stack exceeded error due to recursive behavior. Instead try using setTimeout which is a callback.
Also based on your markup your selector is wrong. it should be #advisersDiv
function fadeIn() {
$('#pulseDiv').find('div#advisersDiv').delay(400).addClass("pulse");
setTimeout(fadeOut,1); //<-- Provide any delay here
};
function fadeOut() {
$('#pulseDiv').find('div#advisersDiv').delay(400).removeClass("pulse");
setTimeout(fadeIn,1);//<-- Provide any delay here
};
fadeIn();