메뉴 건너뛰기




Volumn 7, Issue 1, 1997, Pages 129-146

Basin boundary bifurcations and boundary crisis in the twin-well Duffing oscillator: Scenarios related to the saddle of the large resonant orbit

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0030631531     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127497000091     Document Type: Article
Times cited : (14)

References (22)
  • 1
    • 0001816458 scopus 로고
    • Quantitative universality for a class of nonlinear transformations
    • Feigenbaum, M. J. [1978] "Quantitative universality for a class of nonlinear transformations," J. of Stat. Phys. 19, 25-52.
    • (1978) J. of Stat. Phys. , vol.19 , pp. 25-52
    • Feigenbaum, M.J.1
  • 2
    • 0012349493 scopus 로고
    • Crises, sudden changes in chaotic attractors and transient chaos
    • Grebogi, C., Ott, E. & Yorke, J. A. [1983] "Crises, sudden changes in chaotic attractors and transient chaos," Physica D7, 181-200.
    • (1983) Physica , vol.D7 , pp. 181-200
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 3
    • 45949126663 scopus 로고
    • Basin boundary metamorphoses: Changes in accesible boundary orbits
    • Grebogi, C., Ott, E. & Yorke, J. A. [1987] "Basin boundary metamorphoses: Changes in accesible boundary orbits," Physica D24, 243-262.
    • (1987) Physica , vol.D24 , pp. 243-262
    • Grebogi, C.1    Ott, E.2    Yorke, J.A.3
  • 5
    • 0010750342 scopus 로고
    • Bifurcations of subharmonics in a nonlinear oscillator: Perturbation methods versus numerical experiment
    • eds. Kapitaniak, T. & Brindley, J. (World Scientific, Singapore)
    • Janicki, K. L. &: Szemplińska-Stupnicka, W. [1994] "Bifurcations of subharmonics in a nonlinear oscillator: Perturbation methods versus numerical experiment," in Chaos and Nonlinear Mechanics Series in Nonlinear Science B, Vol. 4, eds. Kapitaniak, T. & Brindley, J. (World Scientific, Singapore), pp. 30-39.
    • (1994) Chaos and Nonlinear Mechanics Series in Nonlinear Science B , vol.4 , pp. 30-39
    • Janicki, K.L.1    Szemplińska-Stupnicka, W.2
  • 6
    • 21844518300 scopus 로고
    • From single well chaos to cross well chaos: A detailed explanation in terms of manifold intersections
    • Katz, A. L. & Dowell, E. H. [1994] "From single well chaos to cross well chaos: A detailed explanation in terms of manifold intersections," Int. J. Bifurcation and Chaos 4(4), 933-941.
    • (1994) Int. J. Bifurcation and Chaos , vol.4 , Issue.4 , pp. 933-941
    • Katz, A.L.1    Dowell, E.H.2
  • 7
    • 0000124206 scopus 로고
    • Basin erosion in the twin-well Duffing oscillator: Two distinct bifurcation scenarios
    • Lansbury, A. N., Thompson, J. M. T. & Stewart, H. B. [1992] "Basin erosion in the twin-well Duffing oscillator: Two distinct bifurcation scenarios," Int. J. Bifurcation and Chaos 2(2), 505-532.
    • (1992) Int. J. Bifurcation and Chaos , vol.2 , Issue.2 , pp. 505-532
    • Lansbury, A.N.1    Thompson, J.M.T.2    Stewart, H.B.3
  • 8
    • 25844520919 scopus 로고
    • Fractal basin boundaries and homoclinic orbits for periodic motion in a two-well potential
    • Moon, F. C. & Li, G.-X. [1985] "Fractal basin boundaries and homoclinic orbits for periodic motion in a two-well potential," Phys. Rev. Lett. 55, 1439-1444.
    • (1985) Phys. Rev. Lett. , vol.55 , pp. 1439-1444
    • Moon, F.C.1    Li, G.-X.2
  • 10
    • 0003582543 scopus 로고
    • Cambridge University Press, Cambridge
    • Ott, E. [1993] Chaos in Dynamical Systems (Cambridge University Press, Cambridge).
    • (1993) Chaos in Dynamical Systems
    • Ott, E.1
  • 11
    • 34250254669 scopus 로고
    • Intermittent transition to turbulence in dissipative dynamical systems
    • Pomeau, Y. & Manneville, P. [1980] "Intermittent transition to turbulence in dissipative dynamical systems," Comm. Math. Phys. 74, 189-199.
    • (1980) Comm. Math. Phys. , vol.74 , pp. 189-199
    • Pomeau, Y.1    Manneville, P.2
  • 12
    • 0029275970 scopus 로고
    • Numerical and geometrical analysis of bifurcations and chaos for an asymmetrical elastic nonlinear oscillator
    • Rega, G., Salvatori, A. & Benedettini, F. [1995] "Numerical and geometrical analysis of bifurcations and chaos for an asymmetrical elastic nonlinear oscillator," Nonlinear Dynamics 7, 249-272.
    • (1995) Nonlinear Dynamics , vol.7 , pp. 249-272
    • Rega, G.1    Salvatori, A.2    Benedettini, F.3
  • 13
    • 0000347179 scopus 로고
    • Strange attractors
    • Ruelle, D. [1980] "Strange attractors," Math. Intell. 12, 126-137.
    • (1980) Math. Intell. , vol.12 , pp. 126-137
    • Ruelle, D.1
  • 14
    • 0000195534 scopus 로고
    • Determination of crisis parameter values by direct observation of manifold tangencies
    • Sommerer, J. C. & Grebogi, C. [1992] "Determination of crisis parameter values by direct observation of manifold tangencies," Int. J. Bifurcation and Chaos 2(2), 383-396.
    • (1992) Int. J. Bifurcation and Chaos , vol.2 , Issue.2 , pp. 383-396
    • Sommerer, J.C.1    Grebogi, C.2
  • 15
    • 0041535046 scopus 로고
    • Catastrophes with indeterminate outcome
    • Stewart, H. B. & Ueda, Y. [1991] "Catastrophes with indeterminate outcome," Proc. R. Soc. London A432, 113-123.
    • (1991) Proc. R. Soc. London , vol.A432 , pp. 113-123
    • Stewart, H.B.1    Ueda, Y.2
  • 16
    • 0000497367 scopus 로고
    • Steady states in the twin-well potential oscillator: Computer simulations and approximate analytical studies
    • Szemplińska-Stupnicka, W. & Rudowski, J. [1993a] "Steady states in the twin-well potential oscillator: Computer simulations and approximate analytical studies," Chaos 3, 375-385.
    • (1993) Chaos , vol.3 , pp. 375-385
    • Szemplińska-Stupnicka, W.1    Rudowski, J.2
  • 17
    • 0000436108 scopus 로고
    • Bifurcations phenomena in a nonlinear oscillator: Approximate analytical studies versus computer simulation results
    • Szemplińska-Stupnicka, W. & Rudowski, J. [1993b] "Bifurcations phenomena in a nonlinear oscillator: Approximate analytical studies versus computer simulation results," Physica D66, 368-380.
    • (1993) Physica , vol.D66 , pp. 368-380
    • Szemplińska-Stupnicka, W.1    Rudowski, J.2
  • 18
    • 0001176745 scopus 로고
    • Cross-well chaos and escape phenomena in driven oscillators
    • Szemplińska-Stupnicka, W. [1992] "Cross-well chaos and escape phenomena in driven oscillators," Nonlinear Dynamics 3, 225-243.
    • (1992) Nonlinear Dynamics , vol.3 , pp. 225-243
    • Szemplińska-Stupnicka, W.1
  • 20
    • 0000974341 scopus 로고
    • Basin explosions and escape phenomena in the twin-well Duffing oscillator: Compound global bifurcations organizing behavior
    • Ueda, Y., Yoshida, S., Stewart, H. B. & Thompson, J. M. T. [1990] "Basin explosions and escape phenomena in the twin-well Duffing oscillator: Compound global bifurcations organizing behavior," Phil. Trans. Roy. Soc. London A332, 169-186.
    • (1990) Phil. Trans. Roy. Soc. London , vol.A332 , pp. 169-186
    • Ueda, Y.1    Yoshida, S.2    Stewart, H.B.3    Thompson, J.M.T.4
  • 21
    • 0021897490 scopus 로고
    • Random phenomena resulting from nonlinearity in the system described by Duffing's equation
    • Ueda, Y. [1985] "Random phenomena resulting from nonlinearity in the system described by Duffing's equation," Int. J. Nonlinear Mechanics 20, 481-491.
    • (1985) Int. J. Nonlinear Mechanics , vol.20 , pp. 481-491
    • Ueda, Y.1
  • 22
    • 0001629622 scopus 로고
    • Survey of regular and chaotic phenomena in the forced Duffing oscillator
    • Ueda, Y. [1991] "Survey of regular and chaotic phenomena in the forced Duffing oscillator," Chaos, Solitons and Fractals 1, 199-231.
    • (1991) Chaos, Solitons and Fractals , vol.1 , pp. 199-231
    • Ueda, Y.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.