Generic saddle-node bifurcation for cascade second order ODEs on manifolds

• Autorzy: Milan Medveď
• Języki publikacji: EN

Abstrakty

EN

Cascade second order ODEs on manifolds are defined. These objects are locally represented by coupled second order ODEs such that any solution of one of them can represent an external force for the other one. A generic saddle-node bifurcation theorem for 1-parameter families of cascade second order ODEs is proved.

Słowa kluczowe

EN

cascade; ODE; critical element; transversal; bifurcation

Kategorie tematyczne

• 35B32: Bifurcation

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Annales Polonici Mathematici
• Rocznik: 1998
• Tom: 68
• Numer: 3
• Strony: 211-225

Daty

wydano

1998

otrzymano

1997-01-23

poprawiono

1997-07-17

Twórcy

autor

Milan Medveď

• Department of Mathematical Analysis, Faculty of Mathematics and Physics, Comenius University, Mlynská dolina, 842 15 Bratislava, Slovakia

Bibliografia

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• [3] M. Medveď, Generic bifurcations of second order ordinary diferential equations on differentiable manifolds, Math. Slovaca 27 (1977), 9-24.
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• [5] M. Medveď, On generic bifurcations of second order ordinary differential equations near closed orbits, Astérisque 50 (1977), 23-29.
• [6] M. Medveď, Fundamentals of Dynamical Systems and Bifurcation Theory, Adam Hilger, Bristol, 1992.
• [7] M. Medveď, A class of vector fields on manifolds containing second order ODEs, Hiroshima Math. J. 26 (1996), 127-149.
• [8] P. Seibert and R. Suarez, Global stabilization of nonlinear cascade systems, Systems Control Lett. 14 (1990), 347-352.
• [9] S. Shahshahani, Second order ordinary differential equations on differentiable manifolds, in: Global Analysis, Proc. Sympos. Pure Math. 14, Amer. Math. Soc., 1970, 265-272.