메뉴 건너뛰기




Volumn , Issue , 2000, Pages 135-147

On global bifurcation theory of polynomial dynamical systems and its applications

Author keywords

Bifurcation; Erugin s two isocline method; Field rotation parameter; Hilbert s 16th Problem; Limit cycle; Perko s planar termination principle; Separatrix cycle; Wintner s principle of natural termination

Indexed keywords


EID: 0004435949     PISSN: None     EISSN: None     Source Type: Book    
DOI: None     Document Type: Chapter
Times cited : (2)

References (32)
  • 6
    • 0000495631 scopus 로고
    • On the Number of Limit Cycles Which Appear with the Variation of the Coefficients from an Equilibrium Point of Focus or Center Type
    • Russian
    • N. N. Bautin, On the Number of Limit Cycles Which Appear with the Variation of the Coefficients from an Equilibrium Point of Focus or Center Type, Matem. Sbor. 30 (1952), 181-196. (Russian)
    • (1952) Matem. Sbor , vol.30 , pp. 181-196
    • Bautin, N.N.1
  • 7
    • 0000113158 scopus 로고
    • Eleven Small Limit Cycles in a Cubic Vector Field
    • H. Zolqdek, Eleven Small Limit Cycles in a Cubic Vector Field, Nonlinearity8 (1995), 843-860.
    • (1995) Nonlinearity , vol.8 , pp. 843-860
    • Zolqdek, H.1
  • 11
    • 84966222045 scopus 로고
    • Global Families of Limit Cycles of Planar Analytic Systems
    • L. M. Perko, Global Families of Limit Cycles of Planar Analytic Systems, Trans. Amer. Math. Soc.322 (1990), 627-656.
    • (1990) Trans. Amer. Math. Soc , vol.322 , pp. 627-656
    • Perko, L.M.1
  • 12
    • 84968487026 scopus 로고
    • Homoclinic Loop and Multiple Limit Cycle Bifurcation Surfaces
    • L. M. Perko, Homoclinic Loop and Multiple Limit Cycle Bifurcation Surfaces, Trans. Amer. Math. Soc.344 (1994), 101-130.
    • (1994) Trans. Amer. Math. Soc , vol.344 , pp. 101-130
    • Perko, L.M.1
  • 13
    • 0002776683 scopus 로고
    • Multiple Limit Cycle Bifurcation Surfaces and Global Families of Multiple Limit Cycles, J
    • L. M. Perko, Multiple Limit Cycle Bifurcation Surfaces and Global Families of Multiple Limit Cycles, J. Differential Equations122 (1995), 89-113.
    • (1995) Differential Equations , vol.122 , pp. 89-113
    • Perko, L.M.1
  • 18
    • 0002338294 scopus 로고    scopus 로고
    • A General Reduction Method for Periodic Solutions in Conservative and Reversible Systems
    • J. Knobloch, A. Vanderbauwhede, A General Reduction Method for Periodic Solutions in Conservative and Reversible Systems, J. Dynam. Differential Equations8 (1996), 71-102.
    • (1996) J. Dynam. Differential Equations , vol.8 , pp. 71-102
    • Knobloch, J.1    Vanderbauwhede, A.2
  • 20
    • 0004376642 scopus 로고
    • Some Questions of Motion Stability and Qualitative Theory of Differential Equations on the Whole
    • Russian
    • N. P. Erugin, Some Questions of Motion Stability and Qualitative Theory of Differential Equations on the Whole, Prikl. Mat. Mekh. 14 (1950), 459-512. (Russian)
    • (1950) Prikl. Mat. Mekh , vol.14 , pp. 459-512
    • Erugin, N.P.1
  • 21
    • 0004435948 scopus 로고
    • Stromgrenschen dynamischen Abschlusprinzips der pe-riodischen Bahngruppen im restringierten Dreikorperproblem
    • A. Wintner, Beweis des E. Stromgrenschen dynamischen Abschlusprinzips der pe-riodischen Bahngruppen im restringierten Dreikorperproblem, Math. Zeitschr.34(1931), 321-349.
    • (1931) Math. Zeitschr , vol.34 , pp. 321-349
    • Wintner, A.1    Beweis Des, E.2
  • 22
    • 0002297362 scopus 로고
    • Limit-Cycles and Rotated Vector Fields
    • G. F. D. Duff, Limit-Cycles and Rotated Vector Fields, Ann. Math 67(1953), 15-31.
    • (1953) Ann. Math , vol.67 , pp. 15-31
    • Duff, G.F.D.1
  • 24
    • 0003351887 scopus 로고
    • Generic Bifurcations of Dynamical Systems
    • M. M. Peixoto, Ed., Academic Press, New York
    • J. Sotomayor, Generic Bifurcations of Dynamical Systems, in Dynamical Systems, M. M. Peixoto, Ed., Academic Press, New York, 1973, pp. 549-560.
    • (1973) Dynamical Systems , pp. 549-560
    • Sotomayor, J.1
  • 26
    • 0000899594 scopus 로고
    • Snakes: Oriented Families of Periodic Orbits, Their Sources, Sinks and Continuation
    • J. Mallet-Paret and J. A. Yorke, Snakes: Oriented Families of Periodic Orbits, Their Sources, Sinks and Continuation, J. Differential Equations43 (1982), 419-450.
    • (1982) J. Differential Equations , vol.43 , pp. 419-450
    • Mallet-Paret, J.1    Yorke, J.A.2
  • 27
    • 0042139163 scopus 로고
    • Bifurcations of Limit Cycles of a Quadratic System with Two Critical Points and Two Field-Rotation Parameters
    • Russian
    • L. A. Cherkas, V. A. Gaiko, Bifurcations of Limit Cycles of a Quadratic System with Two Critical Points and Two Field-Rotation Parameters, Diff. Urameniya 23 (1987), 1544-1553 (Russian)
    • (1987) Diff. Urameniya , vol.23 , pp. 1544-1553
    • Cherkas, L.A.1    Gaiko, V.A.2
  • 28
    • 0004382655 scopus 로고
    • Bifurcations of Limit Cycles of a Quadratic System with Two Critical Points and Two Field-Rotation Parameters
    • L. A. Cherkas, V. A. Gaiko, Bifurcations of Limit Cycles of a Quadratic System with Two Critical Points and Two Field-Rotation Parameters Differential Equations23 (1987), 1062-1069.
    • (1987) Differential Equations , vol.23 , pp. 1062-1069
    • Cherkas, L.A.1    Gaiko, V.A.2
  • 29
    • 0004381531 scopus 로고
    • Separatrix Cycles of Quadratic Systems
    • Russian
    • V. A. Gaiko, Separatrix Cycles of Quadratic Systems, Doklady Akad. Sci. Belarus 37 (1993), 18-21. (Russian)
    • (1993) Doklady Akad. Sci. Belarus , vol.37 , pp. 18-21
    • Gaiko, V.A.1
  • 30
    • 0001085501 scopus 로고    scopus 로고
    • Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems: Problems, Approaches, Conjectures
    • V. A. Gaiko, Qualitative Theory of Two-Dimensional Polynomial Dynamical Systems: Problems, Approaches, Conjectures, Nonlin. Analysis, Theory, Meth. Appl. 30 (1997), 1385-1394.
    • (1997) Nonlin. Analysis, Theory, Meth. Appl , vol.30 , pp. 1385-1394
    • Gaiko, V.A.1
  • 31
    • 85056053838 scopus 로고    scopus 로고
    • Global Qualitative Investigation, Limit Cycle Bifurcations and Applications of Polynomial Dynamical Systems
    • Z. Do, šlá et al., Eds, Masaryk University, Bmo
    • V. A. Gaiko, Global Qualitative Investigation, Limit Cycle Bifurcations and Applications of Polynomial Dynamical Systems, in Papers of the Conference on Differential Equations and Their Applications, Z. Došlá et al., Eds, Masaryk University, Bmo, 1997, pp. 123-130.
    • (1997) Papers of the Conference on Differential Equations and Their Applications , pp. 123-130
    • Gaiko, V.A.1
  • 32
    • 0004449510 scopus 로고    scopus 로고
    • Application of Topological Methods to Qualitative Investigation of Two-Dimensional Polynomial Dynamical Systems
    • V. A. Gaiko, Application of Topological Methods to Qualitative Investigation of Two-Dimensional Polynomial Dynamical Systems, Univ. Iagellonicae Acta Math. 36(1998), 211-214.
    • (1998) Univ. Iagellonicae Acta Math , vol.36 , pp. 211-214
    • Gaiko, V.A.1


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.