×

Bifurcations and trajectories joining critical points. (English) Zbl 0361.34026


MSC:

34C05 Topological structure of integral curves, singular points, limit cycles of ordinary differential equations
34C10 Oscillation theory, zeros, disconjugacy and comparison theory for ordinary differential equations
37-XX Dynamical systems and ergodic theory
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Gilbarg, D., The existence and limit behavior of the one-dimensional shock layer, Amer. J. Math., 7, 256 (1951) · Zbl 0044.21504
[2] Conley, C.; Smoller, J., Viscosity matrices for two-dimensional nonlinear hyperbolic systems, Comm. Pure Appl. Math., 23, 867 (1970) · Zbl 0204.11303
[3] Gordon, P., Paths connecting elementary critical points of dynamical systems, SIAM J. Appl. Math., 26, 35 (1974) · Zbl 0244.34034
[4] Carpenter, G., Travelling wave solutions of nerve impulse equations, (Thesis (1974), University of Wisconsin)
[5] D. G. Aronson and H. F. Weinberger; D. G. Aronson and H. F. Weinberger · Zbl 0325.35050
[6] Foy, R., Steady state solutions of hyperbolic systems of conservation laws with viscosity terms, Comm. Pure Appl. Math., 17, 177 (1964) · Zbl 0178.11902
[7] Friedrichs, K. O.; Hyers, D. H., The existence of solitary waves, Comm. Pure Appl. Math., 7, 517 (1954) · Zbl 0057.42204
[8] Keller, J., The solitary wave and periodic waves in shallow water, Comm. Pure Appl. Math., 1, 323 (1948) · Zbl 0031.33105
[9] J. Marsden; J. Marsden
[10] Ruelle, D.; Takens, F., On the nature of turbulence, Comm. Math. Phys., 20, 167 (1971) · Zbl 0223.76041
[11] Hopf, E., Abzweigung einer periodischen Lösung von einer stationären Lösung eines Differentialsystems, Ber. Math.-Phys. Kl. Sächs. Akad. Wiss. Leipzig, 44, 3 (1942), (L. N. Howard and N. Kopell, Trans. [9]) · Zbl 0063.02065
[12] L. N. Howard and N. Kopell; L. N. Howard and N. Kopell · Zbl 0349.35070
[13] Takens, F., Forced Oscillations, (Applications of global analysis I (1974), Dept. Math. Univ. Utrecht) · Zbl 1156.37315
[14] Arnold, V. I., Lectures on bifurcations in versal families, Russian Math. Surveys, 27, 119 (1972)
[15] Lax, P. D., Hyperbolic systems of conservation laws. II, Comm. Pure Appl. Math., 10, 537 (1957) · Zbl 0081.08803
[16] Conley, C.; Smoller, J., Shock waves as limits of progressive wave solutions of higher order equations, Comm. Pure Appl. Math., 24, 459 (1971) · Zbl 0233.35063
[17] Winfree, A., Rotating solutions to reaction diffusion equations in simply connected media, (Cohen, D. S., Mathematical Aspects of Chemical and Biochemical Problems and Quantum Chemistry. Mathematical Aspects of Chemical and Biochemical Problems and Quantum Chemistry, SIAM-AMS Proc., Vol. 8 (1974), Am. Math. Soc) · Zbl 0322.35046
[18] Kopell, N.; Howard, L. N., Bifurcations under nongeneric conditions, Advances in Math., 13, 274 (1974) · Zbl 0285.34025
[19] Kelley, A., The stable, center stable, center, center-unstable and unstable manifolds, (Abraham, R.; Robbin, J., Transversal Mappings and Flows (1967), Benjamin: Benjamin New York) · Zbl 0173.11001
[20] M. Hirsch, C. Pugh, and M. Shub; M. Hirsch, C. Pugh, and M. Shub
[21] Abraham, R.; Robbin, J., Transversal Mappings and Flows (1967), Benjamin: Benjamin New York · Zbl 0171.44404
[22] Andronow, A. A.; Chaiken, C. E., Theory of Oscillations (1949), Princeton Univ. Press: Princeton Univ. Press Princeton, N. J, Chap. 6
[23] Kopell, N.; Howard, L. N., Plane wave solutions to reaction-diffusion equations, Stud. Appl. Math., 52, 291 (1973) · Zbl 0305.35081
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.