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首页> 外文期刊>Modern Physics Letters, B. Condensed Matter Physics, Statistical Physics, Applied Physics >Near consensus complex linear and nonlinear social networks
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Near consensus complex linear and nonlinear social networks

机译：接近共识的复杂线性和非线性社交网络

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摘要

Some of the nodes of complex social networks may support for a given proposal, while the rest of the nodes may be against the given proposal. Even though all the nodes support for or are against the given proposal, the decision certitudes of individual nodes may be different. In this case, the steady state values of the decision certitudes of the majority of the nodes are either higher than or lower than a threshold value. Deriving the near consensus property is a key to the analysis of the behaviors of complex social networks. So far, no result on the behaviors of the complex social networks satisfying the near consensus property has been reported. Hence, it is useful to extend the definition of the exact consensus property to that of a near consensus property and investigate the behaviors of the complex social networks satisfying the near consensus property. This paper extends the definition of exact consensus complex social networks to that of near consensus complex social networks. For complex linear social networks, this paper investigates the relationships among the vectors representing the steady state values of the decision certitudes of the nodes, the influence weight matrix and the set of vectors representing the initial state values of the decision certitudes of the nodes under a given near consensus specification. The above analysis is based on the Eigen theory. For complex nonlinear social networks with certain types of nonlinearities, the relationship between the influence weight matrix and the vectors representing the steady state values of the decision certitudes of the nodes is studied. When a complex nonlinear social network does not achieve the exact consensus property, the optimal near consensus condition that the complex social network can achieve is derived. This problem is formulated as an optimization problem. The total number of nodes that the decision certitudes of the nodes are either higher than or lower than a threshold value is maximized subject to the corresponding near consensus specification. The optimization problem is a nonsmooth optimization problem. The nonsmooth constraints are first approximated by smooth constraints. Then, the approximated optimization problem is solved via a conventional smooth optimization approach. Computer numerical simulation results as well as the comparisons of the behaviors of complex nonlinear social networks to those of the complex linear social networks are presented. The obtained results demonstrate that some complex social networks can satisfy the near consensus property but not the exact consensus property. Also, the conditions for the near consensus property are dependent on the types of nonlinearities, the influence weight matrix and the vectors representing the initial state values of the decision certitudes of the nodes.
机译：复杂社交网络的某些节点可能支持给定的建议，而其余节点可能与给定的建议相反。即使所有节点都支持或反对给定的建议，各个节点的决策确定度也可能不同。在这种情况下，大多数节点的决策确定性的稳态值高于或低于阈值。得出接近共识的属性是分析复杂社交网络行为的关键。到目前为止，还没有关于满足近乎一致属性的复杂社交网络的行为的结果的报道。因此，将确切的共识属性的定义扩展到接近共识属性的定义，并研究满足该接近共识属性的复杂社会网络的行为，将很有用。本文将精确的共识复杂社交网络的定义扩展到了接近共识复杂社交网络的定义。对于复杂的线性社交网络，本文研究了表示节点决策度的稳态值的向量，影响权重矩阵和表示节点决策度的初始状态值的向量集之间的关系。给出接近共识的规范。以上分析基于本征理论。对于具有某些非线性类型的复杂非线性社会网络，研究了影响权重矩阵与表示节点决策度的稳态值的向量之间的关系。当复杂的非线性社交网络无法实现精确的共识性时，就可以得出复杂社交网络可以实现的最佳接近共识条件。该问题被表述为优化问题。取决于相应的接近共识规范，使节点的决策度高于或低于阈值的节点总数最大化。优化问题是不平滑的优化问题。首先通过平滑约束近似非平滑约束。然后，通过常规的平滑优化方法来解决近似优化问题。给出了计算机数值模拟结果，并对复杂的非线性社交网络与复杂的线性社交网络的行为进行了比较。获得的结果表明，一些复杂的社交网络可以满足近乎共识的属性，但不能满足确切的共识属性。而且，接近共识属性的条件取决于非线性的类型，影响权重矩阵和代表节点决策度初始状态值的向量。

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