On the Global Economic Exploitation Process: Steady States and Stability Aspects for economic Networks with Scale-Free and Limited (Cut-Off) Transitions —The Concrete Case of the European Union

Abstract

The main objective of this Article is to determine the Steady States of two probable economic Scenarios between national economies within the global economic exploitation Process. A mathematical tool extracting the Steady States on the specific Dynamics could be the modeling of appropriate Differential Equations. As Steady States represent solutions that remain unchanged in time evolution, we define these Dynamics Constellations as “Metastability”. However, Metastability can not be identified unconditionally with Economic Stability. We demonstrate in this Article that unrelated Aspects and Criteria could lead to meaningful Concepts for economic Stability (for example, in analyzing the Concept of the small world Networks). Additionally, we point out that Criteria for economic Criticality are often contained in the Metastability Phase in the form of hidden Information. In this Article, we observe two important and probable economic Constellations, which could appear within the global economic Exploitation Process. As we observe and focus on the economic Relations of national economies it is necessary to define at this stage the concept of economic Antagonism. An antagonistic economic environment means that the economic exploitation of the players depends only on their economic strength (power) tending to reach economic Dominance. This economic environment can be compared with a fair sports Discipline while the players have generally different Levels of Ability (competitiveness, Competence) to reach Superiority. In this sense, we look for Steady States using the Lotka-Volterra Model as it seems to be appropriate to simulate such Dynamics. In a further Step, we proceed to consider additively time-fractal Aspects in the classical Lotka-Volterra Differential Equations. In this context, two possible Scenarios within the global economic exploitation Process (Globalization) could be established. The first one is an antagonistic environment in which the exchange of Goods and services is not characterized by any Trade Restrictions. Specifically, the national economies do not impose Customs and one single currency is valid for trade activities. This economic Constellation could be described as a specific economic Alliance between national economies and, in an extreme case, could take the form of a single national economy worldwide, while the word “national” degenerates as not meaningful. Further, the second Scenario within the global exploitation economic Process could consist of a strong protective economic environment in which the Players impose Customs and establish Exchange-currency Strategies or other Trade restrictions in order to control and monitor their Export-Import Relations. Using Concepts of the Econophysics we characterize the first Scenario as a transition-free Environment and the second one as a protective economic Frame. We extract within the first antagonistic Scenario the Steady States with the Help of the Lotka-Volterra Model as the unequal Competitiveness Level of the Players leads to Predator-Pray Dynamics. According to this aim, we define the Competitiveness Level of a national economy by constructing a Rang Scala with appropriate normalized Parameters. In a further Step, we detect economic Instability by analyzing specific Relations within the economic “Small World Networks” concept. Finally, we extract mathematically Steady States considering both Scenarios with the Help of the “topological induced Diffusion” Concept, assuming that the exchange activities of economic Players depend on the environment in which they evolve. We proceed using the fractional Master Equation, which provides Solutions in a purely stochastic sense opening a big window for the interpretation of Steady States in Dynamics. Using the Concept of the topological induced Diffusion we identify the transition-free Scenario as a scale-free Scenario as the economic transitions are assumed to be unlimited. In this case, we assume that the economic Exploitation Process takes place in a superdiffusive environment (Levy Flights). Within the second Scenario, we assume the Existence of Cut-Offs in the Dynamics caused by the diverse trade restrictions. At this stage, it is of interest to observe the Experiences between the single economies of the European Union. The Exchange of Goods and services takes place without important Trade Restrictions representing a very important particular Paradigm in the Globalization Process. However, the E.U. promises economic Cohäsion between the single economies establishing Compensation Funds and other Balance Strategies. This Fact has been respected in this Article by incorporating a specific parameter in the Lotka-Volterra Model. Thus the E.U. economic evolution could stand as a realistic and paradigmatic Concept within the global economic exploitation Process.