Title: A Theory of Complex Stochastic Systems with Two Types of Counteracting Entities,
Abstract: Many complex systems share two characteristics: 1) they are stochastic in
nature, and 2) they are characterized by a large number of factors. At the same
time, various natural complex systems appear to have two types of intertwined
constituents that exhibit counteracting effects on their equilibrium. In this
study, we employ these few characteristics to lay the groundwork for analyzing
such complex systems. The equilibrium point of these systems is generally
studied either through the kinetic notion of equilibrium or its energetic
notion, but not both. We postulate that these systems attempt to regulate the
state vector of their constituents such that both the kinetic and the energetic
notions of equilibrium are met. Based on this postulate, we prove: 1) the
existence of a point such that the kinetic notion of equilibrium is met for the
less abundant constituents and, at the same time, the state vector of more
abundant entities is regulated to minimize the energetic notion of equilibrium;
2) the effect of unboundedly increasing less (more) abundant constituents
stabilizes (destabilizes) the system; and 3) the (unrestricted) equilibrium of
the system is the point at which the number of stabilizing and destabilizing
entities increase unboundedly with the same rate.