The Complexity And The Role Of The Forget And Remember Mechanism In The Spreading System

Complexity science is a new and developing interdisciplinary science nowadays, the purpose of which is the study of nonlinear, non-equilibrium and many-body problems. Its appearance develops non-linear science enormously. The spreading network is one of the most common complex systems, which has been studied adequately, therefore the spreading system is one of complexity science most important research directions. This paper introduces the basic concepts and the basic properties of the complexity network; it also elaborates the main models and the basic properties of spreading system, the common method for spreading system and the new standpoint to classify the spreading system. Based on the above discussion, The forget-remember mechanism (FRM) is proposed. The main work of this article is the research of the spreading system with the FRM, and can be divided into two parts.In the first part, we draw that the objects in the spreading system can be divided into two sorts: things and message. The epidemic system is often composed by some individual nodes, and each node has four states at most. Therefore, we classify the spreading system into: 2-state model, 3-state model and 4-state model, which is the premise for the mathematical expression drawing the spread systems.In the second part, we introduce a new mechanism-the forget-remember mechanism (FRM) into the spreading process. An individual can forget the "message" received and remember the one forgotten in the spreading system with the FRM. Distinguishing from the traditional spreading model, the probability of state switch is governed by linear or exponential forget-remember functions of history time which is measured by the time elapsed since the most recent state change. The present results reveal that the forget-remember mechanism has significant effects on the saturation of message spreading, and may even lead to a termination of spreading under certain conditions. Additionally, it is found that percolation-like phase transitions can occur. By investigating the properties of clusters, formed by connected, active individuals, we may be able to justify the existence of such phase transitions.