Modeling the Influence of External Factors on the Emergence of Specialization in Abstract Systems
- PDF / 156,108 Bytes
- 9 Pages / 612 x 792 pts (letter) Page_size
- 15 Downloads / 166 Views
NTROL SCIENCES
Modeling the Influence of External Factors on the Emergence of Specialization in Abstract Systems F. T. Aleskerov∗,∗∗,a and D. N. Tverskoi∗,∗∗,b ∗
Trapeznikov Institute of Control Sciences, Russian Academy of Sciences, Moscow, Russia ∗∗ Higher School of Economics, National Research University, Moscow, Russia e-mail: a [email protected], b [email protected]. Received July 16, 2018 Revised October 6, 2018 Accepted October 17, 2018
Abstract—We propose a model of specialization in abstract systems with a resource constraint and under the assumption that all structural constraints in the model are linear functions. We study essential properties of solutions to the problem of efficiency maximization of system functioning. We show how and when specialization emerges in the system containing identical elements. Keywords: abstract systems, specialization, resource constraint, structural constraints, efficiency DOI: 10.1134/S0005117920070115
1. INTRODUCTION Since classical works [1, 2], optimization methods are widely used in modeling biological processes. In particular, evolutionary biology explores the issue of the transition from single-celled organisms to multicellular life forms. It is studied how colonial organisms transform in the process of evolution into multicellular forms of life, and what factors influence this process. The colonial organism is arranged as follows: some cells may specialize in a particular function, but do not lose the potential to perform other functions and perform them, for example, in case of changes in external conditions that force this. If conditions that promote full specialization in the colonial organism persist for a sufficiently long period of time, a transition from the colonial form to the multicellular organism is possible. However, the fundamental optimization models of specialization proposed in evolutionary biology [3–5] have a number of fundamental shortcomings. For example, they do not take into account the influence of the environment on the system, although a number of experimental studies show that environmental factors should influence the life activity of the colony [6, 7]. In this paper we improve the models proposed in evolutionary biology by eliminating these shortcomings, and consider these new models already in the context of the theory of abstract systems. We note that the problems considered in this paper belong to the class of problems studied in the framework of system optimization [8]. 2. MODEL Consider an abstract system consisting of N elements. Let i = 1, . . . , N be the indices of elements in the system. Suppose that each item can perform one of two problems. Let us denote through 1307
1308
ALESKEROV, TVERSKOI
bi ∈ [0, bmax ] the level of execution of the first problem by the element with index i. Through i max vi ∈ [0, vi ] we denote the level of execution of the second problem by the element with index i. and vimax are positive real numbers, which can For each element with index i, the quantities bmax i be interpreted as the maximum possible executio
Data Loading...
