Heider balance of a chain of actors as dependent on the interaction range and a thermal noise

Towards the Heider balance -- a cellular automaton with a global neighborhood

“…The same kind of updating was applied in [15] for a local neighborhood. Our approach is complementary to the previous ones [11,12,13,14,15,16]. As we demonstrate below the results obtained within this approach are qualitatively new.…”

“…During this process, the network evolves towards the so-called Heider balance called also structural balance, where the dissonance is removed [8,9,10]. To the best of our knowledge, there are five different algorithms designed to model this process: two Monte-Carlo algorithms [11,12] and three deterministic ones [13,14,15,16]. The first two distinguish only positive (friendly) and negative (hostile) relations.…”

“…The advantage of the latter approach [14] is that the equations may be solved analytically. The last method [15,16] is a deterministic synchronous cellular automaton, where the states of links are updated based on a local rule. Recently the Monte-Carlo simulations [12] have been generalized by including thermal noise [17,18] and a specific aging of the relations [19].…”

“…The rationale behind Eq. 2 is the same as in [11,12,13,14,15,16]. Namely, the relation s ij of i with j is improved, if the relations s ik and s kj are both friendly ("friend of my friend") or both hostile ("enemy of my enemy").…”