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Entering the information era, the formation of public opinion is largely associated with the complex system constructed by the Internet, thereby possessing new characteristics. The formation of public opinion is the result of the interaction of individual behavior with social environment. In reality, the environmental factor and the individual behavior are usually related to each other and co-evolve with time. Based on the Ising model, in this paper established is an opinion formation model that includes the process of the accumulation and digestion of the social tension. In the model, a parameter named effective dissolving factor c is designed to represent the extent of the interaction between the system and the social environment. A two-dimensional dynamical system is involved in the model to describe the dynamics of individual behavior and social tension. The co-evolution behavior of the system is studied. Based on the Landau mean field theory, the stationary states of the dynamical system under different parameter values, i.e. the value of effective dissolving factor c, their stability and bifurcation of the system, are analyzed. Finally, the computer simulation method is used to verify the results. The research shows that with the co-evolution mechanism of the system, our model exhibits certain self-organization characteristics. When the effective dissolving factor c is smaller than the threshold value, the system will reach final consensus opinion, resulting in a macroscopically ordered state. Otherwise, when the dissolving factor c exceeds a threshold value, the system is stable in the disordered state. It is interesting to find that there is such a critical value of the parameter that it leads the system to be self-organized into a critical state from any initial state. The future detailed investigation on the criticality of the co-evolving system is also suggested, such as testing whether the system has evolved into the critical state according to the finite-sized scaling theory and calculating the critical exponent of the system. In addition, in this paper provided is a new perspective to tackle practical problems in public opinion. Based on the mechanism of the formation of public opinion revealed by our model, researchers are encouraged to conduct studies on how to monitor the state of public opinion more precisely and to predict the tipping point of the system evolution.

Cyclical game is often used to study the biodiversity in ecosystem. However, the interaction distance mode considered in previous studies of cyclical game is only the interaction between nearest neighbors, a fixed distance, or a random value of fixed distance among the individuals of species. This is not consistent with the actual situation. In this paper, considering the fact that Levy flight and Brownian motion widespreadly exist in ecosystem, and comprehensively considering the nearest-neighbor-interaction and long-range-interaction given by Levy flight and Brownian motion, the cyclical game and conditions of maintaining biodiversity are investigated. The critical relation of maximal step length of flight versus choosing probability is presented, including Logistic and exponent relations. Further the critical relation between power-law exponent and choosing probability is found. The condition of maintaining species coexistence is also found.

Recently, self-organized oscillation networks have aroused great interest in diverse natural and social fields. Genetic regulatory networks are one of the most typical examples of this kind. They control the growth and develop of organism. We investigate the control of few node genetic regulatory networks. We use a method of multiple phase advanced driving to control the networks, which can improve the control efficiency. The numerical simulation, results show that for the network in which system parameter is fixed, the control efficiency will reach 95% (for 10-node network), and the method will also applicable for the network in which system parameter is unfixed.

Bootstrap percolation was first used in statistic physics to study the phenomenon that magnetic-order goes down and disappears because of the disturbance of nonmagnetic impurity. With the development of complex network, the application of bootstrap percolation in network has attracted much attention. In the real world, many systems naturally exhibit the two-branch structure. And bipartite network is one of important networks in complex networks. In this paper, we use the dynamics equation and computational simulation to study the bootstrap percolation in bipartite networks. The parameters we focus on are the node initial active ratios f1 and f2 and active thresholds Ω1, and Ω2. We draw the conclusion that the ratio of active nodes has discontinuous transition, which will gradually disappear with parameters varying. We also prove the consistency between the dynamic equation and simulation results.

Opinion formation is the result of co-evolution of individual behavior and environment. Individual behavior is determined by its rational cognition and irrational emotion. Environment includes culture, cognitive and behavioral patterns and social interactions. Culture and cognitive patterns are usually related to the spatial factors. In this paper, a social network with geographical factors is constructed. Together with the Ising model in networks, the effects of both spatial and social factors on opinion formation are investigated. The phase transition in the process of opinion formation is studied. The results indicate that both spatial cultural background and global preference for public opinion are crucial to opinion formation.

In this paper, we construct a cost constrained spatial network by adding long-range connections to the one-dimensional circle. The probability for a long-range connection between nodes i and j is pij dij- ( 0), where dij is the lattice distance and the total length of the long-range connections is set to be =cN(c 0), where c is a positive constant and N is the network size. According to the simulation and numeric results, we find an optimal power-law exponent 0 such that the mean first-passage time is shortest. Furthermore, the shortest mean first-passage time has the power law relationships with the network size N. With the increase of network size N and the total cost , the optimal power-law exponent 0 increases monotonically and approaches 1.5.

Weighted networks can give more detailed description of interaction between agents of corresponding systems. Link weight also provides another way to improve the properties and functions of networks. Based on the concept of network efficiency in binary networks, in this paper, the efficiency of weighted networks with similarity or dissimilarity weight is defined. The effect of weight distribution on the network efficiency are investigated. From the initial regular network with homogeneous link weights, a method is introduced to randomize the weight distribution over the links. The results demonstrate that the random redistribution of link weight can improve the network efficiency. Moreover, exponential distribution of link weight shows more significant improvement compared with the other common distributions, such as uniform, Poisson, Gauss, and power law distributions. Meanwhile, it is also found that the total weight of the corresponding minimum spanning tree is reduced with the randomization of link weight. That means the cost of transportation is decreased with the increase of link weight heterogeneity. All these results can help us get deeper understanding about the effect of link weight on the property and function of networks.