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HOMOCLINIC CONNECTIONS NEAR A BELYAKOV POINT IN CHUA'S EQUATION

A. ALGABA

Dept. Mathematics, Fac. Ciencias Experimentales, Univ. Huelva, Avda de las Fuerzas Armadas s/n, 21071 Huelva, Spain

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M. MERINO

Dept. Mathematics, Fac. Ciencias Experimentales, Univ. Huelva, Avda de las Fuerzas Armadas s/n, 21071 Huelva, Spain

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A. J. RODRÍGUEZ-LUIS

Dept. Applied Mathematics II, E.S. Ingenieros, Univ. Sevilla, Camino de los Descubrimientos s/n, 41092 Sevilla, Spain

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https://doi.org/10.1142/S0218127405012739Cited by:7 (Source: Crossref)

Abstract

In this work, the distribution and organization of different homoclinic orbits (double- and triple-pulse) in a ℤ₂-symmetric three-dimensional system are studied in the vicinity of a Belyakov point, that is, a point where the involved equilibrium in the homoclinic connection changes from saddle-node to saddle-focus. The analytical results are successfully applied in the study of such degeneration in Chua's equation.

Keywords:

References

A. Algabaet al., Int. J. Bifurcation and Chaos 10, 291 (2000). Link, Web of Science, Google Scholar
A. Algabaet al., Int. J. Bifurcation and Chaos 13, 583 (2003). Link, Web of Science, Google Scholar
Algaba, A., Merino, M. & Rodríguez-Luis, A. J. [2005] "Homoclinic interactions between T-points and a degenerate homoclinic connection near a triple-zero linear degeneracy in Chua's equation," in preparation . Google Scholar
L. A. Belyakov, Matematicheskie Zametki 15, 336 (1974). Google Scholar
L. A. Belyakov, Matematicheskie Zametki 28, 910 (1980). Web of Science, Google Scholar
L. A. Belyakov, Matematicheskie Zametki 36, 838 (1984). Web of Science, Google Scholar
A. R. Champneys and Y. A. Kuznetsov, Int. J. Bifurcation and Chaos 4, 785 (1994). Link, Web of Science, Google Scholar
Doedel, E. J., Champneys, A. R., Fairgrieve, T. F. Kuznetsov, Y. A., Sandstede, B. & Wang, X. [1998] AUTO97: Continuation and bifurcation software for ordinary differential equations (with HomCont) . Google Scholar
P. Gaspard, Phys. Lett. A 97, 1 (1983). Crossref, Web of Science, Google Scholar
P. Glendinning, Phys. Lett. A 103, 163 (1984). Crossref, Web of Science, Google Scholar
P. Glendinning and C. Sparrow, J. Stat. Phys. 35, 645 (1984). Crossref, Web of Science, Google Scholar
S. V. Gonchenkoet al., Nonlinearity 10, 409 (1997). Crossref, Web of Science, Google Scholar
J. Guckenheimer and P. J. Holmes , Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields ( Springer , Berlin , 1983 ) . Crossref, Google Scholar
A. J. Homburg, Nonlinearity 15, 1029 (2002). Crossref, Web of Science, Google Scholar
Yu. Kuznetsov , Elements of Applied Bifurcation Theory ( Springer-Verlag , NY , 1995 ) . Crossref, Google Scholar
Y. A. Kuznetsov, O. De Feo and S. Rinaldi, SIAM J. Appl. Math. 62, 462 (2001). Crossref, Web of Science, Google Scholar
L. Pivka, C. W. Wu and A. Huang, Int. J. Bifurcation and Chaos 6, 2443 (1996). Link, Web of Science, Google Scholar
L. P. Shil'nikov, Sov. Math. Dokl. 6, 163 (1965). Google Scholar
L. P. Shil'nikov, Math. USSR Sbornik 10, 91 (1970). Crossref, Google Scholar