On perturbations of systems with multidimensional degeneration
Bifurcation conditions are found for the periodic solutions in systems of differential equations with the perturbation (small disturbance) in the case of existence of joined Floke solutions in a linearized nonperturbed system. For this case a multidimensional analog of the Malkin bifurcation function is built up.
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- 1.Malkin, I.G., Nekotorye zadachi teorii nelineinykh kolebanii (Some Problems of the Theory of Nonlinear Oscillations), Moscow: Gos. Izd. Tekh. Teor. Liter., 1956.Google Scholar
- 3.Blekhman, I.I., Sinkhronizatsiya dinamicheskikh system (Synthronization of Dynamic Sistems), Moscow: Nauka, 1971.Google Scholar
- 4.Krasnosel’skii, M.A., Operator sdviga po traektoriyam differentsial’nykh uravnenii (The Shift Operator along Trajectories of Differential Equations), Moscow: Nauka, 1966.Google Scholar
- 5.Akhmerov, R.R., Periodic Solutions of Systems of Autonomous Functionally Differential Equations of the Neutral Type with Small Delay, Diff. Uravn., 1974, vol. 10, no. 11, pp. 1923–1931.Google Scholar
- 6.Aizengendler, P.G., On Bifurcation of Periodic Solutions of Differential Equations with Delay. I, Izv. Vyssh. Uchebn. Zaved., 1969, no. 10, pp. 3–10.Google Scholar
- 7.Aizengendler, P.G., On Bifurcation of Periodic Solutions of Differential Equations with Delay. II, Izv. Vyssh. Uchebn. Zaved., 1969, no. 11, pp. 3–12.Google Scholar
- 8.Kamenskii, M.I., On Bifurcation in the Implicit Function Theorem with Uneven Conditions, in Sovremennye metody teorii kraevykh zadach (Modern Methods of the Theory of Boundary-Value Problems), Voronezh: Voronezh. Gos. Univ., 2009, pp. 79–80.Google Scholar
- 9.Kamenskii, M.I., On Variational Interpretation of the Problem on Bifurcation of Periodic Solution of Differential Equations in the Case of Nonisolated Positions of Equilibrium of the Neutralized Equation, in Voronezh. zimnyaya mat. shk. S.G. Kreina (Krein Voronezh Winter School), Voronezh: Voronezh State Univ., 2010, pp. 74–75.Google Scholar
- 11.Mery nekompaktnosti i uplotnyaushchie operatory (Measures of Noncompactness and Condensing Operators), Akhmerov, R.R. et al., Eds., Novosibirsk: Nauka, 1986.Google Scholar