The Study On Emergence Of Collective Behavior In Swarm Systems

In the animal world,various kinds of collective motions have been found and proven to be efficient ways of carrying out some activities such as searching for food and avoiding predators.Many scholars research the interactions of collective behaviors of human beings according to the rules of collective behaviors of animals.Human factors determine the behavior of people and further influence the interaction of people.The stock market is a kind of the complex systems in which human factors can be investigated based on the interaction of people.In the stock market,traders usually determine their investment strategy not only according to their own viewpoints but also take some advice of others at various degrees.The heterogeneity and irrational behavior of traders in the stock market affect stock price volatility.From the point of view of herding effect that caused by irrational human factors,this paper constructs a model describing the interaction of heterogeneous traders by introducing Lotka-Volterra equation that can properly represent the complex interaction of heterogeneous groups of creatures.From microcosmic view,we analyze the quantitative variation of heterogeneous traders under various degrees of herding effect.On the other hand,from macroscopical view,we explore the relationship among market average rationality,market average investment attitude,stock price and herding effect.The result indicates that: with the increase of herding effect,the investment behavior of heterogeneous traders gradually emerges excessive speculation activities and their decision-making behavior becomes more variable and unfixed.Market average rationality increases slightly at first and then appears the phenomenon of sharply fluctuate.Stock prices gradually deviate from the basic value,which can lead to the decline of stock prices and stock market crash.Besides,plenty of nonlinear and chaotic dynamics are shown in simulation results.Apart from the stock market model,based on the Lennard-Jones potential function and a self-organization process,our paper proposes a topological communication model to simulate the collective behaviors of human beings.In the results of simulations,we find various types of collective behavior and fission behavior and discover the threshold for the emergence of collective behavior,which is the range [5,7] for the number of topology K.According to the analysis of network properties of the model,the in-degree of individuals is always equal to the number of topology.In the stable state,the out-degrees of individuals distribute around the value of the number of topology K,except that the out-degree of a single individual is approximately double the out-degrees of the other individuals.In addition,under different initial conditions,some features of different kinds of networks emerge from the model.We also find the leader and herd mentality effects in the characteristics of the behaviors of human beings in our model.Thus,this work could be used to discover how to promote the emergence of beneficial group behaviors and prevent the emergence of harmful behaviors.