Point-to-periodic and periodic-to-periodic connections

BIT Numerical Mathematics

Volumn 44, Issue 1, 2004, Pages 41-62

  Dieci, Luca ^a   Rebaza, Jorge ^b  

^a GEORGIA INSTITUTE OF TECHNOLOGY   (United States)

^b MISSOURI STATE UNIVERSITY   (United States)

Author keywords

Connecting orbits; Continuation of invariant subspaces; Monodromy matrix; Periodic orbits; Projection boundary conditions

Indexed keywords

EID: 4043102017     PISSN: 00063835     EISSN: None     Source Type: Journal    
DOI: 10.1023/B:BITN.0000025093.38710.f6     Document Type: Article

References (21)

1. D. G. Aronson, E. J. Doedel, and H. G. Othmer, An analytical and numerical study of the bifurcations in a system of linearly-coupled oscillators, Physica D, 25 (1987), pp. 20-104.
2. U. Ascher, R. Mattheij, and R. Russell, Numerical Solution of Boundary Value Problems for Ordinary Differential Equations, Prentice-Hall, 1998.
3. F. Bai, G. Lord, and A. Spence, Numerical computations of connecting orbits in discrete and continuous dynamical systems, Int. J. Bif. Chaos, 6 (1996), pp. 1281-1293.
4. W. J. Beyn, The numerical computation of connecting orbits in dynamical systems, IMA J. Numer. Anal., 9 (1990), pp. 379-405.
5. W. J. Beyn, On well-posed problems for connecting orbits in dynamical systems, Contemp. Math., 172 (1994), pp. 131-168.
6. A. R. Champneys, Y. A. Kuznetsov, and B. Sandstede, A numerical toolbox for homoclinic bifurcation analysis, Int. J. Bif. Chaos, 6 (1996), pp. 867-887.
7. A. R. Champneys and G. J. Lord, Computation of homoclinic solutions to periodic orbits in a reduced water-wave problem, Physica D, 102 (1997), pp. 101-124.
8. S. Coombes, From periodic traveling waves to traveling fronts in the spike-diffuse-spike model of dendritic waves, Math. Biosci., 170 (2001), pp. 155-172.
9. J. Demmel, L. Dieci, and M. Friedman, Computing connecting orbits via an improved algorithm for continuing invariant subspaces, SIAM J. Sci. Comput., 22 (2001), pp. 81-94.
10. L. Dieci and M. Friedman, Continuation of invariant subspaces, Numer. Linear Algebra Appl., 8 (2001), pp. 317-327.
11. L. Dieci and J. Lorenz, Lyapunov-type numbers and torus breakdown: Numerical aspects and a case study, Numer. Algorithms, 14 (1997), pp. 79-102.
12. E. J. Doedel and M. Friedman, Numerical computation of heteroclinic orbits, J. Comp. Appl. Math., 26 (1989), pp. 159-170.
13. E. J. Doedel, M. Friedman, and B. Kunin, Succesive continuation for locating connecting orbits, Numer. Algorithms, 14 (1997), pp. 103-124.
14. E. J. Doedel, A. R. Champneys, T. F. Fairgrieve, Yu. A. Kuznetsov, B. Sandstede, and X. J. Wang, AUTO97, Continuation and bifurcation software for ordinary differential equations (with HomCont), Technical Report, 1997. (ftp.cs.concordia.ca)
15. E. Freire, J. Rodriguez, E. Gamero, and E. Ponce, A case study for homoclinic chaos in an autonomous electronic circuit, Physica D, 62 (1993), pp. 230-243.
16. Ph. Hartman, Ordinary Differential Equations, Wiley, 1964.
17. B. Katzengruber, M. Krupa, and P. Szmolyan, Bifurcation of traveling waves in extrinsic semiconductors, Physica D, 144 (2000), pp. 1-19.
18. W. S. Koon, M. W. Lo, J. E. Marsden, and S. D. Ross, Heteroclinic connections between periodic orbits and resonance transitions in celestial mechanics, Chaos, 10 (2000), pp. 427-469.
19. F. J. Muñoz-Almaraz, E. Freire, J. Galàn, E. Doedel, and A. Vanderbauwhede, Continuation of periodic orbits in conservative and Hamiltonian systems, Physica D, 181 (2003), pp. 1-38.
20. T. Pampel, Numerical approximation of connecting orbits with asymptotic rate, Numer. Math., 90 (2001), pp. 309-348.
21. R. Serban, W. S. Koon, M. Lo, J. E. Marsden, L. R. Petzold, S. D. Ross, and R. S. Wilson, Halo orbit mission correction maneuvers using optimal control, Automatica, 38 (2002), pp. 571-583.