Kamenskii, M. I.; Lysakova, Yu. V.; Nistri, P. On bifurcation of periodic solutions for functional differential equations of the neutral type with small delay. (English. Russian original) Zbl 1155.93027 Autom. Remote Control 69, No. 12, 2027-2032 (2008); translation from Avtom. Telemekh. 2008, No. 12, 41-46 (2008). Summary: The class is singled out of systems described by ordinary differential equations unsolved relative to a derivative, in which a small delay leads to bifurcation of periodic solutions from the equilibrium state. The direct application of the classical results of M. A. Krasnosel’skii to these systems is made difficult in view of the complex character of the dependence on a bifurcation parameter, which is a small delay. The problem on bifurcation of periodic solutions for the stated systems is solved by methods of the theory of rotation of condensing vector fields. Cited in 2 Documents MSC: 93C15 Control/observation systems governed by ordinary differential equations 34K13 Periodic solutions to functional-differential equations 93C10 Nonlinear systems in control theory Keywords:ordinary differential equations; bifurcation of periodic solutions; bifurcation parameter, which is a small delay; rotation of condensing vector fields × Cite Format Result Cite Review PDF Full Text: DOI References: [1] Krasnosel’skii, M.A., Operator sdviga po traektoriyam differentsial’nykh uravnenii (The Operator of Shift by Trajectories of Differential Equations), Moscow: Nauka, 1966. [2] El’sgol’ts, L.E. and Norkin, S.B., Vvedenie v teoriyu differentsial’nykh uravnenii s zapazdyvayuchshim argumentom (Introduction into the Theory of Differential Equations with the Delay Argument), Moscow: Nauka, 1971. [3] Akhmerov, R.R., Kamenskii, M.I., Potapov, A.S., Rodkina, A.E., and Sadovskii, B.N., Measures of Noncompactness and Condensing Operators Basel: Birkhauser, 1992. [4] Rudin, U., Osnovy matematicheskogo analiza (Bases of Mathematical Analysis), St. Petersburg: Lan’, 2002. [5] Vainikko, G.M., Ob approksimatsii lineinykh i nelineinykh operatorov i priblizhennom reshenii operatornykh uravnenii (On Approximation of Linear and Nonlinear Operators and the Approximate Solution of Operator Equations), Tartu: B.I., 1968. [6] Kamenskii, M.I., On Investigation of Stability of Periodic Solutions for a New Class of Systems of Quasilinear Equations in the Banach Space, Dokl. Ross. Akad. Nauk, 1996, vol. 353, no. 1, pp. 13–17. This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.