A Dynamical Model of Decision-Making Behavior in a Network of Consumers with Applications to Energy Choices

A consumer behavior model is considered in the context of a network of interacting individuals in an energy market. We propose and analyze a simple dynamical model of an ensemble of coupled active elements mimicking consumers' behavior, where "word-of-mouth" interactions between individuals are important. A single element is modeled using the automatic control system framework. Assuming local (nearest neighbor) coupling we study the evolution of chains and lattices of the model consumers when varying the coupling strength and initial conditions. The results are interpreted as the dynamics of the decision-making process by the energy-market consumers. We demonstrate that a pitchfork bifurcation to the homogeneous solution leads to bistability of stationary regimes, while the autonomous system is always monostable. In the presence of inhomogeneities, this results in the formation of clusters of sharply positive and negative opinions. We also find that, depending on the coupling strength, the perturbations caused by inhomogeneities can be exponentially localized in space or delocalized. In the latter case, the coarse-graining of opinion clusters occurs.