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Volumn 9, Issue 1, 2010, Pages 89-106

Noise-induced backward bifurcations of stochastic 3D-cycles

Author keywords

Bifurcations; Limit cycles; Roessler system; Stochastic systems

Indexed keywords


EID: 77951693732     PISSN: 02194775     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0219477510000095     Document Type: Article
Times cited : (32)

References (46)
  • 3
    • 0033633360 scopus 로고    scopus 로고
    • Changes in the dynamical behavior of nonlinear systems induced by noise
    • P. S. Landa and P. V. E. McClintock, Changes in the dynamical behavior of nonlinear systems induced by noise, Physics Reports 323 (2000) 1-80.
    • (2000) Physics Reports , vol.323 , pp. 1-80
    • Landa, P.S.1    McClintock, P.V.E.2
  • 5
    • 0039065101 scopus 로고    scopus 로고
    • Stochastic resonance
    • L. Gammaitoni et al., Stochastic resonance, Rev. Mod. Phys. 70 (1998) 223.
    • (1998) Rev. Mod. Phys. , vol.70 , pp. 223
    • Gammaitoni, L.1
  • 8
    • 0008534827 scopus 로고    scopus 로고
    • Noise-induced chaos-order transitions
    • F. Gassmann, Noise-induced chaos-order transitions, Phys. Rev. E 55 (1997) 2215-2221.
    • (1997) Phys. Rev. E , vol.55 , pp. 2215-2221
    • Gassmann, F.1
  • 10
    • 31144434673 scopus 로고    scopus 로고
    • Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems
    • M. A. Zaks, X. Sailer, L. Schimansky-Geier and A. B. Neiman, Noise induced complexity: From subthreshold oscillations to spiking in coupled excitable systems, Chaos 15 (2005) 026117.
    • (2005) Chaos , vol.15 , pp. 026117
    • Zaks, M.A.1    Sailer, X.2    Schimansky-Geier, L.3    Neiman, A.B.4
  • 11
    • 33750248017 scopus 로고    scopus 로고
    • Two-dimensional noise-sustained structures in optics: Theory and experiments
    • G. Agez, P. Glorieux, M. Taki and E. Louvergneaux, Two-dimensional noise-sustained structures in optics: Theory and experiments, Phys. Rev. A 74 (2006) 043814.
    • (2006) Phys. Rev. A , vol.74 , pp. 043814
    • Agez, G.1    Glorieux, P.2    Taki, M.3    Louvergneaux, E.4
  • 12
    • 33746255747 scopus 로고    scopus 로고
    • Front propagation sustained by additive noise
    • M. G. Clerc, C. Falcon and E. Tirapegui, Front propagation sustained by additive noise, Phys. Rev. E 74 (2006) 011303.
    • (2006) Phys. Rev. E , vol.74 , pp. 011303
    • Clerc, M.G.1    Falcon, C.2    Tirapegui, E.3
  • 13
    • 0033901786 scopus 로고    scopus 로고
    • Sensitivity analysis of the stochastically and periodically forced Brusselator
    • I. A. Bashkirtseva and L. B. Ryashko, Sensitivity analysis of the stochastically and periodically forced Brusselator, Physica A 278 (2000) 126.
    • (2000) Physica A , vol.278 , pp. 126
    • Bashkirtseva, I.A.1    Ryashko, L.B.2
  • 14
    • 33745460041 scopus 로고    scopus 로고
    • Stochastic dynamo model for subcritical transition
    • S. Fedotov, I. Bashkirtseva and L. Ryashko, Stochastic dynamo model for subcritical transition, Phys. Rev. E 73 (2006) 066307-066311.
    • (2006) Phys. Rev. E , vol.73 , pp. 066307-066311
    • Fedotov, S.1    Bashkirtseva, I.2    Ryashko, L.3
  • 15
    • 33646321989 scopus 로고
    • The influence of noise on the logistic model
    • G. Mayer-Kress and H. Haken, The influence of noise on the logistic model, J. Stat. Phys. 26 (1981) 149-171.
    • (1981) J. Stat. Phys. , vol.26 , pp. 149-171
    • Mayer-Kress, G.1    Haken, H.2
  • 16
    • 0022524005 scopus 로고
    • Influence of noise on Duffing-van der Pol oscillators
    • W. Ebeling, H. Herzel, W. Richert and L. Schimansky-Geier, Influence of noise on Duffing-van der Pol oscillators, ZAMM 66 (1986) 141.
    • (1986) ZAMM , vol.66 , pp. 141
    • Ebeling, W.1    Herzel, H.2    Richert, W.3    Schimansky-Geier, L.4
  • 17
    • 0026118691 scopus 로고
    • Co-dimension two bifurcations in the presence of noise
    • N. Sri Namachchivaya, Co-dimension two bifurcations in the presence of noise, J. Appl. Mech. 58 (1991) 259.
    • (1991) J. Appl. Mech. , vol.58 , pp. 259
    • Namachchivaya Sri, N.1
  • 18
    • 0030241802 scopus 로고    scopus 로고
    • Stochastic Hopf bifurcation: An example
    • K. R. Schenk-Hoppe, Stochastic Hopf bifurcation: An example, Int. J. Non. Lin. Mech. 31 (1996) 685-692.
    • (1996) Int. J. Non. Lin. Mech. , vol.31 , pp. 685-692
    • Schenk-Hoppe, K.R.1
  • 19
    • 26844463258 scopus 로고    scopus 로고
    • The effect of noise on pitchfork and Hopf bifurcations
    • A. Juel, A. Darbyshire and T. Mullin, The effect of noise on pitchfork and Hopf bifurcations, Proc. R. Soc. Lond. 453 (1997) 2627-2647.
    • (1997) Proc. R. Soc. Lond. , vol.453 , pp. 2627-2647
    • Juel, A.1    Darbyshire, A.2    Mullin, T.3
  • 25
    • 0018982906 scopus 로고
    • Small fluctuations in systems with multiple limit cycles
    • M. Mangel, Small fluctuations in systems with multiple limit cycles, SIAM. J. Appl. Math. 38 (1980) 120.
    • (1980) SIAM. J. Appl. Math. , vol.38 , pp. 120
    • Mangel, M.1
  • 26
    • 9144244517 scopus 로고
    • Effect of noise and perturbations on limit cycle systems
    • C. Kurrer and K. Schulten, Effect of noise and perturbations on limit cycle systems, Physica D 50 (1991) 311-320.
    • (1991) Physica D , vol.50 , pp. 311-320
    • Kurrer, C.1    Schulten, K.2
  • 27
    • 0006276873 scopus 로고
    • Deterministic noise amplifiers
    • R. J. Deissler and J. D. Farmer, Deterministic noise amplifiers, Physica D 55 (1992) 155.
    • (1992) Physica D , vol.55 , pp. 155
    • Deissler, R.J.1    Farmer, J.D.2
  • 31
    • 77951677223 scopus 로고
    • Fluctuations and Sensitivity in Equilibrium Systems, eds. W. Horsthemke and D. K. Kondepudi Springer, Berlin
    • R. Lefever and J. Turner, Sensitivity of a Hopf Bifurcation to External Multiplicative Noise, in Fluctuations and Sensitivity in Equilibrium Systems, eds. W. Horsthemke and D. K. Kondepudi (Springer, Berlin, 1984), pp. 143-149.
    • (1984) Sensitivity of a Hopf Bifurcation to External Multiplicative Noise , pp. 143-149
    • Lefever, R.1    Turner, J.2
  • 32
    • 4243841718 scopus 로고
    • Sensitivity of a Hopf bifurcation to multiplicative colored noise
    • R. Lefever and J. Turner, Sensitivity of a Hopf bifurcation to multiplicative colored noise, Phys. Rev. Lett. 56 (1986) 1631-1634.
    • (1986) Phys. Rev. Lett. , vol.56 , pp. 1631-1634
    • Lefever, R.1    Turner, J.2
  • 33
    • 0001640637 scopus 로고
    • Postponement of Hopf bifurcations by multiplicative colored noise
    • L. Franzoni, R. Mannella, P. McClintock and F. Moss, Postponement of Hopf bifurcations by multiplicative colored noise, Phys. Rev. A 36 (1987) 834.
    • (1987) Phys. Rev. A , vol.36 , pp. 834
    • Franzoni, L.1    Mannella, R.2    McClintock, P.3    Moss, F.4
  • 34
    • 0012154204 scopus 로고    scopus 로고
    • The stochastic Brusselator: Parametric Noise Destroys Hopf Bifurcation
    • in, Springer, New-York
    • L. Arnold, G. Bleckert and K. Schenk-Hoppe, The stochastic Brusselator: Parametric Noise Destroys Hopf Bifurcation, in Stochastic Dynamics, Bremen (Springer, New-York, 1999), pp. 71-92.
    • (1999) Stochastic Dynamics, Bremen , pp. 71-92
    • Arnold, L.1    Bleckert, G.2    Schenk-Hoppe, K.3
  • 35
    • 0024135650 scopus 로고
    • Hopf bifurcation in the presence of both parametric and external stochastic excitations
    • N. Sri. Namachchivaya, Hopf bifurcation in the presence of both parametric and external stochastic excitations, J. Appl. Mech. 110 (1988) 923.
    • (1988) J. Appl. Mech. , vol.110 , pp. 923
    • Namachchivaya, N.1
  • 36
    • 0030290070 scopus 로고    scopus 로고
    • Bifurcation scenarios of the noisy Duffing-van der Pol oscillator
    • K. R. Schenk-Hoppe, Bifurcation scenarios of the noisy Duffing-van der Pol oscillator, Nonlinear Dynamics 11 (1996) 255-274.
    • (1996) Nonlinear Dynamics , vol.11 , pp. 255-274
    • Schenk-Hoppe, K.R.1
  • 37
    • 0032075512 scopus 로고    scopus 로고
    • Stochastic Hopf bifurcation in a biased van der Pol model
    • H. K. Leung, Stochastic Hopf bifurcation in a biased van der Pol model, Physica A 254 (1998) 146-155.
    • (1998) Physica A , vol.254 , pp. 146-155
    • Leung, H.K.1
  • 38
    • 8644249437 scopus 로고    scopus 로고
    • Stability analysis of a noise-induced Hopf bifurcation
    • K. Mallick and P. Marcq, Stability analysis of a noise-induced Hopf bifurcation, Eur. Phys. J. B 36 (2003) 119.
    • (2003) Eur. Phys. J. B , vol.36 , pp. 119
    • Mallick, K.1    Marcq, P.2
  • 39
    • 2542469547 scopus 로고    scopus 로고
    • Noise-induced reentrant transition of the stochastic Duffing oscillator
    • K. Mallick and P. Marcq, Noise-induced reentrant transition of the stochastic Duffing oscillator, Eur. Phys. J. B 38 (2004) 99.
    • (2004) Eur. Phys. J. B , vol.38 , pp. 99
    • Mallick, K.1    Marcq, P.2
  • 40
    • 0000241853 scopus 로고
    • Deterministic nonperiodic flows
    • E. N. Lorenz, Deterministic nonperiodic flows, J. Atmos. Sci. 12 (1963) 139.
    • (1963) J. Atmos. Sci. , vol.12 , pp. 139
    • Lorenz, E.N.1
  • 41
    • 49549126801 scopus 로고
    • An equation for continuous chaos
    • O. E. Roessler, An equation for continuous chaos, Phys. Lett. A 57 (1976) 397.
    • (1976) Phys. Lett. A , vol.57 , pp. 397
    • Roessler, O.E.1
  • 44
    • 20444492357 scopus 로고    scopus 로고
    • Sensitivity and chaos control for the forced nonlinear oscillations
    • I. A. Bashkirtseva and L. B. Ryashko, Sensitivity and chaos control for the forced nonlinear oscillations, Chaos, Solitons and Fractals 26 (2005) 1437-1451.
    • (2005) Chaos, Solitons and Fractals , vol.26 , pp. 1437-1451
    • Bashkirtseva, I.A.1    Ryashko, L.B.2
  • 45
    • 1642295601 scopus 로고    scopus 로고
    • Sensitivity analysis of stochastically forced Lorenz model cycles under period-doubling bifurcations
    • I. A. Bashkitseva and L. B. Ryashko, Sensitivity analysis of stochastically forced Lorenz model cycles under period-doubling bifurcations, Dyn. Syst. Appl. 11 (2002) 293-309.
    • (2002) Dyn. Syst. Appl. , vol.11 , pp. 293-309
    • Bashkitseva, I.A.1    Ryashko, L.B.2
  • 46
    • 17044372304 scopus 로고    scopus 로고
    • The analysis of the stochastically forced periodic attractors for Chua's circuit
    • M. Ryagin and L. Ryashko, The analysis of the stochastically forced periodic attractors for Chua's circuit, Int. J. Bifurcat. Chaos 14 (2004) 3981-3987.
    • (2004) Int. J. Bifurcat. Chaos , vol.14 , pp. 3981-3987
    • Ryagin, M.1    Ryashko, L.2


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.