Keywords
- Vector Field
- Periodic Orbit
- Equilibrium Point
- Hopf Bifurcation
- Bifurcation Point
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References
Andronov, A.A., Leontovich, E.A., Gordon, I.I. and A.G. Maier, Theory of Bifurcations in the Plane. Wiley, 1973.
Andronov, A.A. and L. Pontrjagin, Systemes grossiers, Dokl. Akad. Nauk. SSSR 14 (1937), 247–251.
Arnol'd, V.I., Lectures on bifurcation in versal families. Russian Math. Surveys, 27 (1972), 54–123.
Bogdanov, R.I., Versal deformations of a singular point of a vector field on the plane in the case of two zero eigenvalues. Func. Anal. Appl. 9 (1975), 144–145; Ibid, 10(1976), 61–62.
Carr, J., Applications of Centre Manifold Theory, Appl. Math. Sci. Vol. 35, 1981, Springer-Verlag, New York.
Cesari, L., Functional analysis, nonlinear differential equations and the alternative method, in Nonlinear Functional Analysis and its Applications (Eds. Cesari, Kannan and Schur), Dekker, New York, 1976, 1–197.
Chow, S.-N. and J.K. Hale, Methods of Bifurcation Theory, Grund. der Math. Wissen., Vol. 251, Springer-Verlag, New York, Heidelberg, Berlin, 1982.
Chow, S.-N., Hale, J.K. and J. Mallet-Paret, An example of bifurcation to homoclinic orbits. J. Differential Eqns. 37 (1980), 351–373.
Conley, C.C., Hyperbolic invariant sets and shift automorphisms, in Dynamical Systems Theory and Applications (Ed., J. Moser), Lecture Notes in Physics 38 (1975), 539–549.
Coppel, W.A., Dichotomies in Stability Theory, Lecture Notes in Math. 629 (1978), Springer-Verlag.
Crandall, M.G. and P.H. Rabinowitz, Bifurcation from a simple eigenvalue, J. Funct. Anal. 8(1971), 321–340.
_____, Bifurcation, perturbation of simple eigenvalues and linearized stability, Arch. Rat. Mech. Anal. 52(1973), 161–180.
deOliveira, J.C. and J.K. Hale, Dynamic behavior from bifurcation equations, Tôhoku Math. J. 32(1980), 189–199.
Golubitsky, M. and V. Guillemin, Stable Mappings and Their Singularities, Springer-Verlag, Berlin, 1973.
Golubitsky, M. and D. Schaeffer, Bifurcation analysis near a double eigenvalue of a model chemical reactor, Arch. Rat. Mech. Anal. 75(1981), 315–348.
Hale, J.K., Theory of Functional Differential Equations, Appl. Math. Sciences 3(1977), Springer-Verlag.
Henry, D., Geometric Theory of Semilinear Parabolic Equations, Lecture Notes in Math., Springer-Verlag, 840(1981).
Holmes, P.J., Averaging and chaotic motion in forced oscillations, SIAM J. Appl. Math. 38(1980), 65–80.
Howard, L.N. and N. Koppell, Bifurcations and trajectories joining critical points, Adv. Math. 18(1976), 306–358.
Kielhöfer, H., Generalized Hopf bifurcation in Hilbert space, Math. Meth. Appl. Sci. 1(1979), 498–513.
Marsden, J. and M.F. McCracken, The Hopf Bifurcation and Its Applications, Springer-Verlag, New York, 1976.
Moser, J., Stable and Random Motions in Dynamical Systems, Princeton Univ. Press, Princeton, N.J., 1973.
Palmer, K.J., Exponential dichotomies and transversal homoclinic points, J. Differential Eqns. To appear.
Pecelli, G., Dichotomies for linear functional differential equations, J. Differential Eqns. 9(1971), 555–579.
Peixoto, M., Structural stability on two dimensional manifolds, Topology 1(1962), 101–120.
Śil'nikov, L.P., On a Poincaré-Birkhoff problem, Mat. Sbornik 74(116), (1967); Math. USSR-Sbornik 3(1967), 353–371.
Smale, S., Differentiable dynamical systems, Bull. Am. Math. Soc. 73(1967), 747–817.
Sotomayor, J., Generic one parameter families of vector fields on two-dimensional manifolds, Publ. Math. I.H.E.S. 43(1974), 5–46.
Takens, F., Singularities of functions and vector fields, Nieuw Arch. Wisk. 20(1972), 107–130.
_____, Forced oscillations and bifurcations in Application of Global Analysis, Communication 3, Math. Inst., Rijksuniversiteit, Utrecht (1974).
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Hale, J.K. (1984). Introduction to dynamic bifurcation. In: Salvadori, L. (eds) Bifurcation Theory and Applications. Lecture Notes in Mathematics, vol 1057. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098595
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DOI: https://doi.org/10.1007/BFb0098595
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