| A variety of systems evolve towards achieving a global organization or coordination without a centralized process or control. As the systems evolve they tend to reach a certain level of harmony and may exhibit a significant robustness towards perturbations. This type of behavior can be observed in many natural systems. This type of system is quite common in our society as well. It is very easy to think of such social systems as networks whose nodes are the people or social groups, while the social relationships represent the links between the nodes.;In this work we use a Cellular Automata and Boolean Network approach to model a social network. We will focus on a Cellular Automata neighborhood approach, where each node is linked to its nearest neighbors. We are interested to know how the happiness spreads throughout the network over time. This type of study has been done before under various network scenarios, but a mathematical model for the time evolution fraction of happiness in the network of a social behavior has not been discussed in related literature. We will show that this mathematical model is suitable for the network under consideration and we specify the parameter values that lead to a good fit of the model. We use the model to assess the dynamics of the network.;We show that under the particulars specified in this work, the network reaches mostly stability: all people are happy or all are sad, so there is consensus. Under a simple noise procedure, the network does not reach consensus anymore; however there is a convergence towards a more or less stable fraction of happy people in the network. The convergence to a stable behavior may take a few hundred steps of iterations. Clusters of happiness or sadness may form in the network. |
