Computer-generated proofs of phase portraits for planar systems

International Journal of Bifurcation and Chaos in Applied Sciences and Engineering

Volumn 6, Issue 5, 1996, Pages 889-892

  Guckenheimer, John ^a   Malo, Salvador ^a  

^a Department of Molecular Biology and Genetics   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 0030135927     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127496000497     Document Type: Article

References (8)

1. Arnold, V. I. [1977] "Loss of stability of self-oscillations close to resonance and versal deformations of equivariant vector fields," Funct. Anal. Appl. 11(2), 1-10.
2. Beresovskaya, F. S. & Khibnik, A. I. [1980] "On separatrices bifurcations in the problem of auto-oscillations stability loss at resonance 1:4," Prikl. Math. Mech. 44, 938-943.
3. Duff, G. F. D. [1953] "Limit-cycles and rotated vector fields," Ann. Math. 57(1), 15-31.
4. Henrici, P. [1962] Discrete Variable Methods in Ordinary Differential Equations (J. Wiley & Sons).
5. Krauskopf, B. [1993] "Bifurcation sequences at 1:4 resonance: An inventory," Technical Report W9308, Department of Mathematics, University of Gröningen.
6. Lloyd, N. G. [1988] "Limit cycles of polynomial systems - some recent developments," New Directions in Dynamical Systems, London Math. Soc. Lecture Note Series, Vol. 127 (Cambridge University Press).
7. Malo, S. [1994] Rigorous Computer Verification of Planar Vector Field Structure (Doctoral Thesis, Cornell University, Ithaca, New York).
8. Neištadt, A. I. [1978] "Bifurcations of phase portraits of a system of differential equations arising in the problem of auto-oscillations stability loss at 1:4 resonance," Prikl. Math. Mech. 42, 830-840.