Human populations act like collections of particles, which makes methods from physics and mathematics a useful frame work to study collective social phenomena and systems. Many methods in particle dynamics apply to social phenomena. Statistical physics, methods to study stochastic processes, stochastic differential equations, game theory, and graph theory are examples of methods that provide a framework to study social phenomena and systems. Such methods are used to study cascade behaviors in traffic, pandemics, crime, voting, opinion dynamics, and rumor spreading. In this sense finding social analogies of physical models like temperature in the Ising model is an active research field. When it comes to human interactions, most of these concepts, ideas, and methods may be classified under social physics. Another approach to the study of such processes is data management. The flow of information and ideas between people is a key process in social physics. The combination of ideas and the spread of new ideas create behavioral changes. Two key concepts that model these processes are exploration and imitation. Consider a population of human individuals. Their opinion and behavior are subject to stochastic and noisy information they get from the media, such as newspapers, TV, and smartphone apps. They also may imitate their friends, colleagues, or co-workers. Individuals can communicate with each other, exchange ideas, and modify their decisions. Imitation is widely used in models based on game theory to study social, biological, and economic behavior. In this paper, the competition between exploration and imitation in a population of individuals is studied and analyzed. It is preva‎lent to assume any individual imitating another adopts the entire opinion of the role model. However, real individuals rarely replace personal opinions with that of others. Instead, an individual partially adapts the opinion of peers, adjusting them as needed. We shall henceforth refer to this behavior as soft imitation. We show that soft imitation changes the dynamics significantly. Complex behavior most often emerges from collections of individuals interrelated within a network with high complexity, great size, an irregular structure, or a dynamic structure. A network can describe both physical structures and interactions. Examples include a biological organism, a social network, and the Worldwide Web. This paper describes our model's behavior on a network, where nodes depict individuals and links represent possible interactions, especially imitations. Following the common methodology, the model is applied on several networks, and the emerging behavior is observed.

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فرهاد فضيله , رضا جعفري , ابوالفضل رمضان پور