ISSN 0021-3454 (print version)
ISSN 2500-0381 (online version)

12
Issue
vol 63 / December, 2020
Article

DOI 10.17586/0021-3454-2019-62-9-851-859

UDC 519.7: 658.512.2

## BIOLOGICAL MODEL FOR FINDING SOLUTIONS TO AN INVENTIVE PROBLEM

A. B. Bushuev
ITMO University, Department of Control Systems and Informatics; Associate Professor

V. Y. Bazhin
St. Petersburg Mining University, Depart-ment of Technological Process Automation and Production;

Y. V. Litvinov
ITMO University, Saint Petersburg, 197101, Russian Federation; Senior lecturer

V. A. Petrov
ITMO University, Department of Computer Science and Control Systems; Post-Graduate Student

O. K. Mansurova
University of Mines, Department of Technological Process Automation and Production; Associate Professor

Abstract. The process of solving an inventive problem by the known specialized algorithm involves transition from a prototype to technical contradiction between two alternative properties. Therefore, the process is considered as a homeostatic binary division of a biological cell. The mathematical model is the Lorentz attractor, for which it is shown that the energy graphs of both mother-daughter homeostats coincide. An example of solving the inventive problem in the Benard experiment, in which the contradictions between the temperature and the velocity of the particle flow are found, is given. The resolution of the contradiction leads to a violation of symmetry and the appearance of closed convection loops. To estimate the attractor asymmetry, a new numerical method for calculating the structure of a system of nonlinear differential equations is proposed. Based on a system of equations in the basis of physical coordinates, an information-energy scheme of the attractor is constructed, for which the concepts of matrices of input and output signals, as well as transfer matrices of blocks are introduced. The scheme does not depend on the initial and boundary conditions, as well as the numerical values of the attractor coefficients, but only on the physical dimensions of the inputs and outputs of the blocks. The graphical representation of the structure with transfer matrices allows to find the vertical axis of the attractor symmetry and to determine the degree of asymmetry in the relations of resource consumption of the left and the right parts.
Keywords: the Lorenz attractor, energy homeostasis, binary cell division, evaluation of the asymmetry of the structure, ARIZ, prototype, technical contradiction

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