We study message spreading on a scale-free network, by introducing a novel forget-remember mechanism. Message, a general term which can refer to email, news, rumor or disease, etc, can be forgotten and remembered by its holder. The way the message is forgotten and remembered is governed by the forget and remember function, F and R, respectively. Both F and R are functions of history time t concerning individual's previous states, namely being active (with message) or inactive (without message). Our systematic simulations show at the low transmission rate whether or not the spreading can be eff...
