ISSN 0869-6632 (Print)
ISSN 2542-1905 (Online)


For citation:

Anisimova S. А. Nonlinear models of reflexive control theory. Izvestiya VUZ. Applied Nonlinear Dynamics, 2004, vol. 12, iss. 1, pp. 96-113. DOI: 10.18500/0869-6632-2004-12-1-96-113

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Russian
Article type: 
Article
UDC: 
159.9:51:530.182:536.75

Nonlinear models of reflexive control theory

Autors: 
Anisimova Svetlana Александровна, Moscow Institute of Physics and Technology
Abstract: 

The work is devoted to mathematical modeling of reflective processes - intensively developing branch of mathematical psychology. A systematical statement of subject models is given in the work where the subject faces а moral choice, i.e. а choice of one of two polar alternatives: first personifies good, and the second - evil. A new, linear-square-law model of subject is offered, which allows combining nonlinear account of the subject’s self-reflection and his opinion on actions of his partner, described in the linear way. A linear description of the partner appears to be natural because оп the one hand it appreciably simplifies the model, оп the other hand а person can estimate his own actions more subtly and in a more complicated manner than his partner’s. The episode from Dostoyevskiy’s novel «Karamazoff brothers» is analyzed within the framework of the advanced model. Important influence of the subject optimism index on the accomplished choice is demonstrated and one of the most important Christian principles «Don’t worry» is illustrated.

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Acknowledgments: 
The work was supported by the RFBR, project № 02-06-80219.
Reference: 

1. Lefebvre VA. Algebra of Conscience. Moscow: Cogito-Center; 2003. 426 p.

2. Lefebvre VA. Algebra of Conscience. Moscow: Kogito-Tsentr Publ.; 2003. 426 p.

3. Dostoyevsky FM. The Brothers Karamazov. Moscow: EKSMO-Press; 2000. 800 p.

4. Anisimova SA. Psychotechnologies in Religious Organisations and the Reflexion theory. Preprint, Inst. Appl. Math., the Russian Academy of Science; 2003;60.

5. Anisimova SA. Linear-quadratic Model of Reflexive Choice. Reflective Processes and Management. Moscow: Kogito-Tsentr Publ.; 2003;3(2).

Received: 
08.07.2003
Accepted: 
29.01.2004
Published: 
20.06.2004