Eur. Phys. J. B 74, 251-263 (2010)
https://doi.org/10.1140/epjb/e2010-00053-2

Coevolution of competing systems: local cooperation and global inhibition

¹ Departamento de Electrónica y Comunicaciones, Facultad de Ingeniería, Universidad de Los Andes, La Hechicera, Mérida, Mérida 5251, Venezuela
² Centro de Física Fundamental, Facultad de Ciencias, Universidad de Los Andes, Apartado Postal 26, La Hechicera, Mérida, Mérida 5251, Venezuela

Corresponding author: parravan@ula.ve

Received: 15 April 2009
Revised: 5 January 2010
Published online: 16 February 2010

Abstract

Using a set of heterogeneous competing systems with intra-system cooperation and inter-system aggression, we show how the coevolution of the system parameters (degree of organization and conditions for aggression) depends on the rate of supply of resources . The model consists of a number of units grouped into systems that compete for the resource S; within each system several units can be aggregated into cooperative arrangements whose size is a measure of the degree of organization in the system. Aggression takes place when the systems release inhibitors that impair the performance of other systems. Using a mean field approximation we show that i) even in the case of identical systems there are stable inhomogeneous solutions; ii) a system steadily producing inhibitors needs large perturbations to leave this regime; and iii) aggression may give comparative advantages. A discrete model is used in order to examine how the particular configuration of the units within a system determines its performance in the presence of aggression. We find that full-scale, one sided aggression is only profitable for less-organized systems, and that systems with a mixture of degrees of organization exhibit robustness against aggression. By using a genetic algorithm we find that, in terms of the full-occupation resource supply rate , the coevolution of the set of systems displays the following behavior: i) for aggressions are irrelevant and most systems exhibit a high degree of organization; ii) For aggressions are frequent, making systems with a low degree of organization competitive; iii) for the systems display global evolutive transitions between periods of calm (few aggressions and high degree of organization) and periods of belligerence (frequent aggressions and low degree of organization); iv) for the periods of aggression becomes progressively rarer and shorter. Finally, when approaches the selection pressure on the cooperativity and the aggression between systems disappears. This kind of model can be useful to analyse the interplay of the cooperation/competition processes that can be found in some social, economic, ecological and biochemical systems; as an illustration we refer to the competition between drug-selling gangs.