Speciality:
05.13.01 (System analysis, the control and processing of information (separated by fields))
Birth date:
30.04.1955
Website: https://www.krasnoselskii.iitp.ru Keywords: nonlinear analysis,
ordinary differential equations,
bifurcations,
nonlinear resonance,
periodic oscillations,
hysteresis.
Subject:
Methods of analysis of degenerated nonlinear operator equations of Hammerstein type with normal linear part were presented. These methods are applicable to the solution of various nonlocal problems on forced oscillations in nonlinear control systems. The theory of periodic oscillations in system with hysteresis was developed. The new method to study Andronov–Hopf bifurcations was presented; the method allow to study variouse degenerate cases and to obtain conditions of existence of cycles and their continua (in collaboration with D. I. Rachinskii). A new class of systems (systems with incomplete corrections) was considered together with Mark Krasnosel'skii and Nikolai Kuznetsov. Various stability conditions of such systems were obtained, these system include so-called "asynchronous systems" as a partial case.
Main publications:
Krasnosel'skii A. M. "Asymptotics of nonlinearities and operator equations". Ser. "Operator Theory", vol. 76, Birkhauser, 1995.
Krasnosel'skii A. M., Pokrovskii A. V. On subharmonics bifurcation in equations with homogeneous nonlinearities. Discrete and Continuous Dynamical Systems, 7, no. 7, 100–114, 2001.
Krasnosel'skii A. M., Mennicken R., Rachinskii D. I. Cycle stability for Hopf bifurcation, generated by sublinear terms. Mathematische Nachrichten, v. 233–234, 171–195, 2002.
Krasnosel'skii A. M., Mennicken R., Rachinskii D. I. Small solutions generated by sublinear terms. Journal of Differential Equations, v. 179, 97–132, 2002.
Krasnosel'skii A. M., Rachinskii D. I. On a bifurcation governed by hysteresis nonlinearity. Nonlinear Differential Equations and Applications, v. 9, 93–115, 2002.
