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JOURNALS // Itogi Nauki i Tekhniki. Sovremennaya Matematika i ee Prilozheniya. Tematicheskie Obzory // Archive

Itogi Nauki i Tekhniki. Sovrem. Mat. Pril. Temat. Obz., 2022 Volume 216, Pages 29–43 (Mi into1078)

Bifurcations in a dynamic system modeling pedagogical impacts on a group of students with a negative informal leader

S. A. Belman, E. Yu. Liskina

Ryazan State University S. A. Esenin

Abstract: We consider a system of ordinary differential equations, which describes a model of the pedagogical impact on a group of students. The impact is expressed as the sum of a constant and a control parameter. We find equilibrium states of the system and determine the types of their bifurcations that arise when the control parameter changes. Also, we obtain coefficient conditions for the emergence of stable equilibrium states and the corresponding bifurcation values of the parameter.

Keywords: differential equation, equilibrium state, control parameter, bifurcation, periodic solution.

UDC: 517.925.41

MSC: 34C23, 37G10, 91F99

DOI: 10.36535/0233-6723-2022-216-29-43



© Steklov Math. Inst. of RAS, 2025