메뉴 건너뛰기




Volumn 18, Issue 4, 2008, Pages 1029-1050

Center bifurcation for two-dimensional border-collision normal form

Author keywords

Border collision bifurcations; Border collision normal forms; Center bifurcation; Piecewise linear 2D maps

Indexed keywords

ECONOMICS; EIGENVALUES AND EIGENFUNCTIONS; PHASE SPACE METHODS; PIECEWISE LINEAR TECHNIQUES;

EID: 45449105557     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/S0218127408020823     Document Type: Article
Times cited : (71)

References (33)
  • 1
    • 0000780796 scopus 로고    scopus 로고
    • Border-collision bifurcations in two-dimensional piecewise smooth maps
    • Banerjee, S. & Grebogi, C. [1999] "Border-collision bifurcations in two-dimensional piecewise smooth maps," Phys. Rev. E 59, 4052-4061.
    • (1999) Phys. Rev. E , vol.59 , pp. 4052-4061
    • Banerjee, S.1    Grebogi, C.2
  • 2
    • 0034156883 scopus 로고    scopus 로고
    • Bifurcations in one-dimensional piecewise smooth maps - theory and applications in switching circuits
    • Banerjee, S., Karthik, M. S., Yuan, G. & Yorke, J. A. [2000a] "Bifurcations in one-dimensional piecewise smooth maps - theory and applications in switching circuits," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 47, 389-394.
    • (2000) IEEE Trans. Circuits Syst.-I: Fund. Th. Appl , vol.47 , pp. 389-394
    • Banerjee, S.1    Karthik, M.S.2    Yuan, G.3    Yorke, J.A.4
  • 3
    • 0033698914 scopus 로고    scopus 로고
    • Bifurcations in 2D piecewise smooth maps - theory and applications in switching circuits
    • Banerjee, S., Ranjan, P. & Grebogi, C. [2000b] "Bifurcations in 2D piecewise smooth maps - theory and applications in switching circuits," IEEE Trans. Circuits Syst.-I: Fund. Th. Appl. 47, 633-643.
    • (2000) IEEE Trans. Circuits Syst.-I: Fund. Th. Appl , vol.47 , pp. 633-643
    • Banerjee, S.1    Ranjan, P.2    Grebogi, C.3
  • 4
    • 0033229544 scopus 로고    scopus 로고
    • Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems
    • Di Bernardo, M., Feigen, M. I., Hogan, S. J. & Homer, M. E. [1999] "Local analysis of C-bifurcations in n-dimensional piecewise smooth dynamical systems," Chaos Solit. Fract. 10, 1881-1908.
    • (1999) Chaos Solit. Fract , vol.10 , pp. 1881-1908
    • Di Bernardo, M.1    Feigen, M.I.2    Hogan, S.J.3    Homer, M.E.4
  • 5
    • 0038351322 scopus 로고    scopus 로고
    • Multiple attractor bifurcations: A source of unpredictability in piecewise smooth systems
    • Dutta, M., Nusse, H. E., Ott, E., Yorke, J. A. & Yuan, G. H. [1999] "Multiple attractor bifurcations: A source of unpredictability in piecewise smooth systems," Phys. Rev. Lett. 83, 4281-4284.
    • (1999) Phys. Rev. Lett , vol.83 , pp. 4281-4284
    • Dutta, M.1    Nusse, H.E.2    Ott, E.3    Yorke, J.A.4    Yuan, G.H.5
  • 6
    • 0034134395 scopus 로고    scopus 로고
    • Nonlinear dynamics of bandpass sigma-delta modulation. An investigation by means of the critical lines tool
    • Feely, O., Fournier-Prunaret, D., Taralova-Roux, I. & Fitzgerald, D. [2000] "Nonlinear dynamics of bandpass sigma-delta modulation. An investigation by means of the critical lines tool," Int. J. Bifurcation and Chaos 10, 303-327.
    • (2000) Int. J. Bifurcation and Chaos , vol.10 , pp. 303-327
    • Feely, O.1    Fournier-Prunaret, D.2    Taralova-Roux, I.3    Fitzgerald, D.4
  • 7
    • 0035421582 scopus 로고    scopus 로고
    • Lowpass sigma-delta modulation: An analysis by means of the critical lines tool
    • Fournier-Prunaret, D., Feely, O. & Taralova-Roux, I. [2001] "Lowpass sigma-delta modulation: An analysis by means of the critical lines tool," Nonlin. Anal. 47, 5343-5355.
    • (2001) Nonlin. Anal , vol.47 , pp. 5343-5355
    • Fournier-Prunaret, D.1    Feely, O.2    Taralova-Roux, I.3
  • 8
    • 0242636637 scopus 로고    scopus 로고
    • Hicks' trade cycle revisited: Cycles and bifurcations
    • Gallegati, M., Gardini, L., Puu, T. & Sushko, I. [2003] "Hicks' trade cycle revisited: Cycles and bifurcations," Math. Comput. Simul. 63, 505-527.
    • (2003) Math. Comput. Simul , vol.63 , pp. 505-527
    • Gallegati, M.1    Gardini, L.2    Puu, T.3    Sushko, I.4
  • 9
    • 26944458790 scopus 로고    scopus 로고
    • Dangerous bifurcation at border collision: When does it occur?
    • 1-4
    • Ganguli, A. & Banerjee, S. [2005] "Dangerous bifurcation at border collision: When does it occur?" Phys. Rev. E 71, 057202 (1-4).
    • (2005) Phys. Rev. E , vol.71 , pp. 057202
    • Ganguli, A.1    Banerjee, S.2
  • 10
    • 45449115501 scopus 로고    scopus 로고
    • The Hick-sian model with investment floor and income ceiling
    • eds. Puu, T. & Sushko, I, Springer-Verlag, NY, pp
    • Gardini, L., Puu, T. & Sushko, I. [2006a] "The Hick-sian model with investment floor and income ceiling," in Business Cycles Dynamics. Models and Tools, eds. Puu, T. & Sushko, I. (Springer-Verlag, NY), pp. 179-192.
    • (2006) Business Cycles Dynamics. Models and Tools , pp. 179-192
    • Gardini, L.1    Puu, T.2    Sushko, I.3
  • 11
    • 84891425677 scopus 로고    scopus 로고
    • A goodwintype model with a piecewise linear investment function
    • eds. Puu, T. & Sushko, I, Springer-Verlag, NY, pp
    • Gardini, L., Puu, T. & Sushko, I. [2006b] "A goodwintype model with a piecewise linear investment function," in Business Cycles Dynamics. Models and Tools, eds. Puu, T. & Sushko, I. (Springer-Verlag, NY), pp. 317-333.
    • (2006) Business Cycles Dynamics. Models and Tools , pp. 317-333
    • Gardini, L.1    Puu, T.2    Sushko, I.3
  • 13
    • 1642601666 scopus 로고    scopus 로고
    • Robust dangerous border-collision bifurcations in piecewise smooth systems
    • 1-4
    • Hassouneh, M. A., Abed, E. H. & Nusse, H. E. [2004] "Robust dangerous border-collision bifurcations in piecewise smooth systems," Phys. Rev. Lett. 92, 070201 (1-4).
    • (2004) Phys. Rev. Lett , vol.92 , pp. 070201
    • Hassouneh, M.A.1    Abed, E.H.2    Nusse, H.E.3
  • 15
    • 0007382289 scopus 로고
    • Period three to period two bifurcations for piecewise linear models
    • Hommes, C. H. & Nusse, H. [1991] "Period three to period two bifurcations for piecewise linear models," J. Econ. 54, 157-169.
    • (1991) J. Econ , vol.54 , pp. 157-169
    • Hommes, C.H.1    Nusse, H.2
  • 16
    • 11744278171 scopus 로고    scopus 로고
    • Multiple choice bifurcations as a source of unpredictability in dynamical systems
    • Kapitaniak, T. & Maistrenko, Y. L. [1998] "Multiple choice bifurcations as a source of unpredictability in dynamical systems," Phys. Rev. E 58, 5161-5163.
    • (1998) Phys. Rev. E , vol.58 , pp. 5161-5163
    • Kapitaniak, T.1    Maistrenko, Y.L.2
  • 17
    • 14844336939 scopus 로고    scopus 로고
    • Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps
    • Kowalczyk, P. [2005] "Robust chaos and border-collision bifurcations in non-invertible piecewise-linear maps," Nonlinearity 18, 485-504.
    • (2005) Nonlinearity , vol.18 , pp. 485-504
    • Kowalczyk, P.1
  • 21
    • 0032131474 scopus 로고    scopus 로고
    • About two mechanisms of reunion of chaotic attractors
    • Maistrenko, Y., Sushko, I. & Gardini, L. [1998] "About two mechanisms of reunion of chaotic attractors," Chaos Solit. Fract. 9, 1373-1390.
    • (1998) Chaos Solit. Fract , vol.9 , pp. 1373-1390
    • Maistrenko, Y.1    Sushko, I.2    Gardini, L.3
  • 22
    • 0003805342 scopus 로고
    • World Scientific, Singapore
    • Mira, C. [1987] Chaotic Dynamics (World Scientific, Singapore).
    • (1987) Chaotic Dynamics
    • Mira, C.1
  • 23
    • 44049121950 scopus 로고
    • Border-collision bifurcations including 'period two to period three' for piecewise smooth systems
    • Nusse, H. E. & Yorke, J. A. [1992] "Border-collision bifurcations including 'period two to period three' for piecewise smooth systems," Physica D 57, 39-57.
    • (1992) Physica D , vol.57 , pp. 39-57
    • Nusse, H.E.1    Yorke, J.A.2
  • 24
    • 4344639901 scopus 로고
    • Border-collision bifurcations for piecewise smooth one-dimensional maps
    • Nusse, H. E. & Yorke, J. A. [1995] "Border-collision bifurcations for piecewise smooth one-dimensional maps," Int. J. Bifurcation and Chaos 5, 189-207.
    • (1995) Int. J. Bifurcation and Chaos , vol.5 , pp. 189-207
    • Nusse, H.E.1    Yorke, J.A.2
  • 25
    • 0038147436 scopus 로고    scopus 로고
    • The Hicksian floor-roof model for two regions linked by interregional trade
    • Sushko, I., Puu, T. & Gardini, L. [2003] "The Hicksian floor-roof model for two regions linked by interregional trade," Chaos Solit. Fract. 18, 593-612.
    • (2003) Chaos Solit. Fract , vol.18 , pp. 593-612
    • Sushko, I.1    Puu, T.2    Gardini, L.3
  • 26
    • 23844524438 scopus 로고    scopus 로고
    • Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps
    • Sushko, I., Agliari, A. & Gardini, L. [2005] "Bistability and border-collision bifurcations for a family of unimodal piecewise smooth maps," Discr. Contin. Dyn. Syst. Series B 5, 881-897.
    • (2005) Discr. Contin. Dyn. Syst. Series B , vol.5 , pp. 881-897
    • Sushko, I.1    Agliari, A.2    Gardini, L.3
  • 27
    • 85126449414 scopus 로고    scopus 로고
    • Sushko, I., Agliari, A. & Gardini, L. [2006] Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves, in Dynamic Modelling in Economics and Finance in Honour of Professor Carl Chiarella, eds. Bischi, G. I. & Sushko, I., Chaos Solit. Fract. 29, 756-770.
    • Sushko, I., Agliari, A. & Gardini, L. [2006] "Bifurcation structure of parameter plane for a family of unimodal piecewise smooth maps: Border-collision bifurcation curves," in Dynamic Modelling in Economics and Finance in Honour of Professor Carl Chiarella, eds. Bischi, G. I. & Sushko, I., Chaos Solit. Fract. 29, 756-770.
  • 28
    • 40549140224 scopus 로고    scopus 로고
    • Center bifurcation for a 2D piecewise linear map
    • eds. Puu, T. & Sushko, I, Springer-Verlag, NY, pp
    • Sushko, I. & Gardini, L. [2006] "Center bifurcation for a 2D piecewise linear map," in Business Cycles Dynamics. Models and Tools, eds. Puu, T. & Sushko, I. (Springer-Verlag, NY), pp. 49-78.
    • (2006) Business Cycles Dynamics. Models and Tools , pp. 49-78
    • Sushko, I.1    Gardini, L.2
  • 29
    • 0036857045 scopus 로고    scopus 로고
    • Dynamical study of a second order DPCM transmission system modeled by a piece-wise linear function
    • Taralova-Roux, I. & Fournier-Prunaret, D. [2002] "Dynamical study of a second order DPCM transmission system modeled by a piece-wise linear function," IEEE Trans. Circuits Syst.-I 49, 1592-1609.
    • (2002) IEEE Trans. Circuits Syst.-I , vol.49 , pp. 1592-1609
    • Taralova-Roux, I.1    Fournier-Prunaret, D.2
  • 32
    • 33745711667 scopus 로고    scopus 로고
    • Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation
    • Zhusubaliyev, Z. T., Mosekilde, E., Maity, S., Mohanan, S. & Banerjee, S. [2006] "Border collision route to quasiperiodicity: Numerical investigation and experimental confirmation," Chaos 16, 023122.
    • (2006) Chaos , vol.16 , pp. 023122
    • Zhusubaliyev, Z.T.1    Mosekilde, E.2    Maity, S.3    Mohanan, S.4    Banerjee, S.5
  • 33
    • 33846080097 scopus 로고    scopus 로고
    • Quasiperiodicity and torus breakdown in a power electronic dc/dc converter
    • Zhusubaliyev, Z. T., Soukhoterin, E. & Mosekilde, E. [2007] "Quasiperiodicity and torus breakdown in a power electronic dc/dc converter," Math. Comput. Simul. 73, 364-377.
    • (2007) Math. Comput. Simul , vol.73 , pp. 364-377
    • Zhusubaliyev, Z.T.1    Soukhoterin, E.2    Mosekilde, E.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.