Interacting herding model: memory and oblivion

The interacting herding model only includes the affects of the last activity and ignores all the activities before. In real market, agents have a long-range time memory about the past activities which affects actually the current one. But, due to oblivion, the past activities have different influences on the current one depending on the time line. In the paper, a long-range memory is introduced to the interacting herding model in which the past activities affect the current one with exponential decay which reflects the fact that agents have a long-range time memory and mislay along with time about the past activities. The numerical calculation shows that its dynamics behaviors exhibit some characteristics more close to the real markets and can include the previous model as a limit case.