Department of Physics, Shahid Beheshti University, Tehran, Iran.
Irkutsk National Research Technical University, Irkutsk, Russia.
PLoS One. 2023 Aug 4;18(8):e0289543. doi: 10.1371/journal.pone.0289543. eCollection 2023.
The competitive balance model was proposed as an extension of the structural balance theory, aiming to account for heterogeneities observed in real-world networks. In this model, different paradigms lead to form different friendship and enmity. As an example, friendship or enmity between countries can have a political or religious basis. The suggested Hamiltonian is symmetrical between paradigms. Our analyses show that a balanced state can be achieved if just one paradigm prevails in the network and the paradigm shift is possible only by imposing an external field. In this paper, we investigate the influence of the external field on the evolution of the network. We drive the mean-field solutions of the model and verify the accuracy of our analytical solutions by performing Monte-Carlo simulations. We observe that the external field breaks the symmetry of the system. The response of the system to this external field, contingent upon temperature, can be either paramagnetic or ferromagnetic. We observed a hysteresis behavior in the ferromagnetic regime. Once communities are formed based on a certain paradigm, then they resist change. We found that to avoid wasting energy we need to know the level of stochastic behavior in the network. Analogous to magnetic systems, we observe that susceptibility adheres to Curie's law.
竞争平衡模型是对结构平衡理论的扩展，旨在解释现实世界网络中观察到的异质性。在这个模型中，不同的范式导致了不同的友谊和敌意。例如，国家之间的友谊或敌意可能有政治或宗教基础。建议的哈密顿量在范式之间是对称的。我们的分析表明，如果网络中只有一种范式占主导地位，并且只有通过施加外部场才能实现范式转变，那么就可以达到平衡状态。在本文中，我们研究了外部场对网络演化的影响。我们推导了模型的平均场解，并通过执行蒙特卡罗模拟验证了我们解析解的准确性。我们观察到外部场打破了系统的对称性。系统对外部场的响应，取决于温度，可以是顺磁性的或铁磁性的。我们在铁磁区域观察到滞后行为。一旦根据某个范式形成了社区，那么它们就会抵制变化。我们发现，为了避免浪费能量，我们需要知道网络中的随机行为水平。类似于磁系统，我们观察到磁化率遵守居里定律。
