메뉴 건너뛰기




Volumn 206, Issue 1-2, 2005, Pages 82-93

Homoclinic snaking near a heteroclinic cycle in reversible systems

Author keywords

Bifurcation; Boussinesq system; Heteroclinic cycle; Homoclinic snaking; Lin's method

Indexed keywords

BIFURCATION (MATHEMATICS); COMPUTATIONAL METHODS; HAMILTONIANS; MATHEMATICAL MODELS; THEOREM PROVING; VECTORS; WAVE EQUATIONS;

EID: 19944412544     PISSN: 01672789     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.physd.2005.04.018     Document Type: Article
Times cited : (87)

References (27)
  • 1
    • 0000327541 scopus 로고    scopus 로고
    • A Boussinesq system for two-way propagation of nonlinear dispersive waves
    • J.L. Bona, and M. Chen A Boussinesq system for two-way propagation of nonlinear dispersive waves Physica D 116 1998 191 224
    • (1998) Physica D , vol.116 , pp. 191-224
    • Bona, J.L.1    Chen, M.2
  • 2
    • 0011913755 scopus 로고    scopus 로고
    • Boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory
    • J.L. Bona, M. Chen, and J.-C. Saut Boussinesq equations and other systems for small amplitude long waves in nonlinear dispersive media I: Derivation and the linear theory J. Nonlinear Sci. 12 2002 283 318
    • (2002) J. Nonlinear Sci. , vol.12 , pp. 283-318
    • Bona, J.L.1    Chen, M.2    Saut, J.-C.3
  • 3
    • 0000654735 scopus 로고    scopus 로고
    • Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics
    • A.R. Champneys Homoclinic orbits in reversible systems and their applications in mechanics, fluids and optics Physica D 112 1-2 1998 158 186
    • (1998) Physica D , vol.112 , Issue.1-2 , pp. 158-186
    • Champneys, A.R.1
  • 4
    • 85064294041 scopus 로고    scopus 로고
    • Solitary-wave and multi-pulsed travelling-wave solutions of Boussinesq systems
    • M. Chen Solitary-wave and multi-pulsed travelling-wave solutions of Boussinesq systems Appl. Anal. 75 1-2 2000 213 240
    • (2000) Appl. Anal. , vol.75 , Issue.1-2 , pp. 213-240
    • Chen, M.1
  • 5
    • 0000598042 scopus 로고
    • The bifurcation of homoclinic and periodic orbits from two heteroclinic orbits
    • S.-N. Chow, B. Deng, and D. Terman The bifurcation of homoclinic and periodic orbits from two heteroclinic orbits SIAM J. Math. Anal. 21 1 1990 179 204
    • (1990) SIAM J. Math. Anal. , vol.21 , Issue.1 , pp. 179-204
    • Chow, S.-N.1    Deng, B.2    Terman, D.3
  • 6
    • 0039015620 scopus 로고    scopus 로고
    • Coalescence of reversible homoclinic orbits causes elliptic resonance
    • B. Fiedler, and D. Turaev Coalescence of reversible homoclinic orbits causes elliptic resonance Int. J. Bifurcation Chaos 6 1996 1007 1027
    • (1996) Int. J. Bifurcation Chaos , vol.6 , pp. 1007-1027
    • Fiedler, B.1    Turaev, D.2
  • 7
    • 22244440263 scopus 로고    scopus 로고
    • Cascades of reversible homoclinic orbits to a bi-focus equilibrium
    • J. Härterich Cascades of reversible homoclinic orbits to a bi-focus equilibrium Physica D 112 1998 187 200
    • (1998) Physica D , vol.112 , pp. 187-200
    • Härterich, J.1
  • 8
    • 33645786256 scopus 로고    scopus 로고
    • Multiple homoclinic orbits in conservative and reversible systems
    • in press
    • A.J. Homburg, J. Knobloch. Multiple homoclinic orbits in conservative and reversible systems. Trans. Am. Math. Soc., in press.
    • Trans. Am. Math. Soc.
    • Homburg, A.J.1    Knobloch, J.2
  • 13
    • 0032478448 scopus 로고    scopus 로고
    • Homotopy classes for stable connections between Hamiltonian Saddle-focus equilibria
    • W.D. Kalies, J. Kwapisz, and R.C.A.M. VanderVorst Homotopy classes for stable connections between Hamiltonian Saddle-focus equilibria Comm. Math. Phys. 193 2 1998 337 371
    • (1998) Comm. Math. Phys. , vol.193 , Issue.2 , pp. 337-371
    • Kalies, W.D.1    Kwapisz, J.2    Vandervorst, R.C.A.M.3
  • 16
    • 0002236568 scopus 로고    scopus 로고
    • Homo- and heteroclinic orbits, hyperbolic subsets in a one-parameter unfolding of a Hamiltonian system with heteroclinic contour with two saddle-foci
    • L.M. Lerman Homo- and heteroclinic orbits, hyperbolic subsets in a one-parameter unfolding of a Hamiltonian system with heteroclinic contour with two saddle-foci Regular Chaotic Dyn. 2 3-4 1997 139 155
    • (1997) Regular Chaotic Dyn. , vol.2 , Issue.3-4 , pp. 139-155
    • Lerman, L.M.1
  • 17
    • 84972438215 scopus 로고
    • Using Melnikovs method to solve Shilnikovs problems
    • X.B. Lin Using Melnikovs method to solve Shilnikovs problems Proc. Roy. Soc. Edinburgh 116A 1990 295 325
    • (1990) Proc. Roy. Soc. Edinburgh , vol.116 , pp. 295-325
    • Lin, X.B.1
  • 18
    • 0003567524 scopus 로고
    • Verzweigungstheorie homokliner Verdopplungen
    • B. Sandstede, Verzweigungstheorie homokliner Verdopplungen, IAAS Report No. 7, 1993.
    • (1993) IAAS Report No. 7 , vol.7
    • Sandstede, B.1
  • 19
    • 3142624970 scopus 로고    scopus 로고
    • Instability of localized buckling modes in a one-dimensional strut model
    • B. Sandstede Instability of localized buckling modes in a one-dimensional strut model Phil. Trans. R. Soc. London A355 1998 2083 2097
    • (1998) Phil. Trans. R. Soc. London , vol.355 , pp. 2083-2097
    • Sandstede, B.1
  • 20
    • 21944451412 scopus 로고    scopus 로고
    • Stability of multi-pulse solutions
    • B. Sandstede Stability of multi-pulse solutions Trans. Am. Math. Soc. 350 2 1998 429 472
    • (1998) Trans. Am. Math. Soc. , vol.350 , Issue.2 , pp. 429-472
    • Sandstede, B.1
  • 21
    • 0030136341 scopus 로고    scopus 로고
    • On the complex Bifurcation set for a system with simple dynamics
    • M.V. Shashkov, and D.V. Turaev On the complex Bifurcation set for a system with simple dynamics Int. J. Bif. Chaos 6 5 1996 949 968
    • (1996) Int. J. Bif. Chaos , vol.6 , Issue.5 , pp. 949-968
    • Shashkov, M.V.1    Turaev, D.V.2
  • 22
    • 0001234956 scopus 로고
    • A case of the existence of a countable number of periodic motions
    • L.P. Shilnikov A case of the existence of a countable number of periodic motions Sov. Math. Dokl. 6 1965 163 166
    • (1965) Sov. Math. Dokl. , vol.6 , pp. 163-166
    • Shilnikov, L.P.1
  • 24
    • 0011175612 scopus 로고
    • Heteroclinic cycles and periodic orbits in reversible systems
    • Ordinary and Delay Differential Equations
    • A. Vanderbauwhede. Heteroclinic cycles and periodic orbits in reversible systems, in: Ordinary and Delay Differential Equations, Pitman Res. Notes Math. Ser. 272 (1992) 250-253.
    • (1992) Pitman Res. Notes Math. Ser. , vol.272 , pp. 250-253
    • Vanderbauwhede, A.1
  • 25
    • 0000034625 scopus 로고
    • Homoclinic period blow-up in reversible and conservative systems
    • A. Vanderbauwhede, and B. Fiedler Homoclinic period blow-up in reversible and conservative systems Z. Angew. Math. Phys. 43 1992 292 318
    • (1992) Z. Angew. Math. Phys. , vol.43 , pp. 292-318
    • Vanderbauwhede, A.1    Fiedler, B.2
  • 26
    • 0346500773 scopus 로고    scopus 로고
    • Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation
    • P.D. Woods, and A.R. Champneys Heteroclinic tangles and homoclinic snaking in the unfolding of a degenerate reversible Hamiltonian-Hopf bifurcation Physica D 129 1999 147 170
    • (1999) Physica D , vol.129 , pp. 147-170
    • Woods, P.D.1    Champneys, A.R.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.