On the validity of use of physical equations and principles in the socio-economic field and on the predictability of socio-economic system dynamics

Abstract

Abstract. Usually, the various empirical and semi-empirical equations and mathematical models are used to study the dynamics of socio-economic systems. In this case, there are very often questions related to the validity of application of such equations and models.In this paper, it is shown that the dynamics of socio-economic systems can be described by mathematical equations analogous to the motion equations that are well known in physics (particularly in classical mechanics). In this connection, it is possible to say that the predictability of the dynamics of a socio-economic system is described by the motion equations (i.e., Newton's equations) to the same degree that these equations predict the dynamics of the physical system. Such models allow us to determine the trends of development in the dynamics of socio-economic systems. The importance of this investigation in using adequate mathematical models is that they allow us to notice those or other adverse trends in the socio-economic systems, therefore, ensuring timely optimal management decisions.

Differential geometric structure of non-equilibrium dynamics in competition and predation: Finsler geometry and KCC theory

“…These interactions can be considered non-linear processes, so there has been some interest in ecological stability against several perturbations, such as environmental change and evolution (e.g., [18,19,17]). The Lotka-Volterra equation is one well-known equation that describes non-linear interactions such as intraspecific or interspecific competition, and predation between prey and predators (e.g., [13,4]). From the Lotka-Volterra equation, we can derive a second-order differential equation that describes ecological interactions (e.g., [5,8,30]).…”