Selected Topics of Social Physics: Nonequilibrium Systems

Abstract

This paper is devoted to nonequilibrium systems in the physics approach to social systems. Equilibrium systems have been considered in the recenly published first part of the review. The style of the paper combines the features of a tutorial and a review, which, from one side, makes it simpler to read for nonspecialists aiming at grasping the basics of social physics, and from the other side, describes several rather recent original models containing new ideas that could be of interest to experienced researchers in the field.

Discrete versus Continuous Algorithms in Dynamics of Affective Decision Making

“…Also, the considered equations are not autonomous and contain time delay. In addition, even if the fixed points would be the same, the stability conditions of discrete, continuous, and delay equations, generally, are different [73][74][75]. Thus, numerical investigations are necessary.…”

“…The probabilities, by definition, are bounded, hence Lagrange stable. Then, for a plane motion, the Poincare-Bendixson theorem tells us that if a trajectory of a continuous two-dimensional dynamical system is Lagrange stable, then it approaches either a stable node or a limit cycle [75]. However, for discrete equations, there is no such theorem, and a discrete dynamical system can exhibit chaos.…”