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Volumn 341, Issue 2, 2008, Pages 834-854

The period function of the generalized Lotka-Volterra centers

Author keywords

Bifurcation; Center; Critical period; Period function

Indexed keywords


EID: 38949134467     PISSN: 0022247X     EISSN: 10960813     Source Type: Journal    
DOI: 10.1016/j.jmaa.2007.10.053     Document Type: Article
Times cited : (20)

References (37)
  • 2
    • 38249035274 scopus 로고
    • The monotonicity of the period function for planar Hamiltonian vector fields
    • Chicone C. The monotonicity of the period function for planar Hamiltonian vector fields. J. Differential Equations 69 (1987) 310-321
    • (1987) J. Differential Equations , vol.69 , pp. 310-321
    • Chicone, C.1
  • 3
    • 38249029275 scopus 로고
    • Geometric methods of two-point nonlinear boundary value problem
    • Chicone C. Geometric methods of two-point nonlinear boundary value problem. J. Differential Equations 72 (1988) 360-407
    • (1988) J. Differential Equations , vol.72 , pp. 360-407
    • Chicone, C.1
  • 4
    • 84966216689 scopus 로고
    • A quadratic system with a nonmonotonic period function
    • Chicone C., and Dumortier F. A quadratic system with a nonmonotonic period function. Proc. Amer. Math. Soc. 102 (1988) 706-710
    • (1988) Proc. Amer. Math. Soc. , vol.102 , pp. 706-710
    • Chicone, C.1    Dumortier, F.2
  • 5
    • 0011628950 scopus 로고
    • Finiteness for critical periods of planar analytic vector fields
    • Chicone C., and Dumortier F. Finiteness for critical periods of planar analytic vector fields. Nonlinear Anal. 20 (1993) 315-335
    • (1993) Nonlinear Anal. , vol.20 , pp. 315-335
    • Chicone, C.1    Dumortier, F.2
  • 6
    • 0000539993 scopus 로고
    • Bifurcation of critical periods for plane vector fields
    • Chicone C., and Jacobs M. Bifurcation of critical periods for plane vector fields. Trans. Amer. Math. Soc. 312 (1989) 433-486
    • (1989) Trans. Amer. Math. Soc. , vol.312 , pp. 433-486
    • Chicone, C.1    Jacobs, M.2
  • 7
    • 0039971668 scopus 로고    scopus 로고
    • Isochronous centers in planar polynomial systems
    • Christopher C.J., and Devlin C.J. Isochronous centers in planar polynomial systems. SIAM J. Math. Anal. 28 (1997) 162-177
    • (1997) SIAM J. Math. Anal. , vol.28 , pp. 162-177
    • Christopher, C.J.1    Devlin, C.J.2
  • 8
    • 0034693569 scopus 로고    scopus 로고
    • Period function for a class of Hamiltonian systems
    • Cima A., Gasull A., and Mañosas F. Period function for a class of Hamiltonian systems. J. Differential Equations 168 (2000) 180-199
    • (2000) J. Differential Equations , vol.168 , pp. 180-199
    • Cima, A.1    Gasull, A.2    Mañosas, F.3
  • 9
  • 10
    • 84972541905 scopus 로고
    • The period function of a Hamiltonian quadratic system
    • Coppel W.A., and Gavrilov L. The period function of a Hamiltonian quadratic system. Differential Integral Equations 6 (1993) 1357-1365
    • (1993) Differential Integral Equations , vol.6 , pp. 1357-1365
    • Coppel, W.A.1    Gavrilov, L.2
  • 11
  • 12
    • 3543103219 scopus 로고    scopus 로고
    • First derivative of the period function with applications
    • Freire E., Gasull A., and Guillamon A. First derivative of the period function with applications. J. Differential Equations 204 (2004) 139-162
    • (2004) J. Differential Equations , vol.204 , pp. 139-162
    • Freire, E.1    Gasull, A.2    Guillamon, A.3
  • 13
    • 0031172970 scopus 로고    scopus 로고
    • An explicit expression of the first Liapunov and period constants with applications
    • Gasull A., Guillamon A., and Mañosa V. An explicit expression of the first Liapunov and period constants with applications. J. Math. Anal. Appl. 211 (1997) 190-212
    • (1997) J. Math. Anal. Appl. , vol.211 , pp. 190-212
    • Gasull, A.1    Guillamon, A.2    Mañosa, V.3
  • 14
    • 38949180665 scopus 로고    scopus 로고
    • The period function for second-order quadratic ODEs is monotone
    • Gasull A., Guillamon A., and Villadelprat J. The period function for second-order quadratic ODEs is monotone. Qual. Theory Dyn. Syst. 5 (2004) 201-224
    • (2004) Qual. Theory Dyn. Syst. , vol.5 , pp. 201-224
    • Gasull, A.1    Guillamon, A.2    Villadelprat, J.3
  • 15
    • 18144392723 scopus 로고    scopus 로고
    • On the period of the limit cycles appearing in one-parameter bifurcations
    • Gasull A., Mañosa V., and Villadelprat J. On the period of the limit cycles appearing in one-parameter bifurcations. J. Differential Equations 213 (2005) 255-288
    • (2005) J. Differential Equations , vol.213 , pp. 255-288
    • Gasull, A.1    Mañosa, V.2    Villadelprat, J.3
  • 16
    • 0002487294 scopus 로고
    • Behaviour of the period of solutions of certain plane autonomous systems near centers
    • Loud W.S. Behaviour of the period of solutions of certain plane autonomous systems near centers. Contrib. Differential Equations 3 (1964) 21-36
    • (1964) Contrib. Differential Equations , vol.3 , pp. 21-36
    • Loud, W.S.1
  • 17
    • 0001228987 scopus 로고    scopus 로고
    • Darboux linearization and isochronous centers with a rational first integral
    • Mardešić P., Moser-Jauslin L., and Rousseau C. Darboux linearization and isochronous centers with a rational first integral. J. Differential Equations 134 (1997) 216-268
    • (1997) J. Differential Equations , vol.134 , pp. 216-268
    • Mardešić, P.1    Moser-Jauslin, L.2    Rousseau, C.3
  • 18
    • 0242371793 scopus 로고    scopus 로고
    • On the time function of the Dulac map for families of meromorphic vector fields
    • Mardešić P., Marín D., and Villadelprat J. On the time function of the Dulac map for families of meromorphic vector fields. Nonlinearity 16 (2003) 855-881
    • (2003) Nonlinearity , vol.16 , pp. 855-881
    • Mardešić, P.1    Marín, D.2    Villadelprat, J.3
  • 20
    • 33745881370 scopus 로고    scopus 로고
    • On the return time function around monodromic polycycles
    • Marín D., and Villadelprat J. On the return time function around monodromic polycycles. J. Differential Equations 228 (2006) 226-258
    • (2006) J. Differential Equations , vol.228 , pp. 226-258
    • Marín, D.1    Villadelprat, J.2
  • 21
    • 0001309891 scopus 로고
    • Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan: mise sous forme normale
    • Bifurcations of Planar Vector Fields. Luminy, 1989, Springer, Berlin
    • Mourtada A. Cyclicité finie des polycycles hyperboliques de champs de vecteurs du plan: mise sous forme normale. Bifurcations of Planar Vector Fields. Luminy, 1989. Lecture Notes in Math. vol. 1455 (1990), Springer, Berlin 272-314
    • (1990) Lecture Notes in Math. , vol.1455 , pp. 272-314
    • Mourtada, A.1
  • 22
    • 84920547916 scopus 로고
    • The periods of the Volterra-Lokta system
    • Rothe F. The periods of the Volterra-Lokta system. J. Reine Angew. Math. 355 (1985) 129-138
    • (1985) J. Reine Angew. Math. , vol.355 , pp. 129-138
    • Rothe, F.1
  • 23
    • 21144464848 scopus 로고
    • Remarks on periods of planar Hamiltonian systems
    • Rothe F. Remarks on periods of planar Hamiltonian systems. SIAM J. Math. Anal. 24 (1993) 129-154
    • (1993) SIAM J. Math. Anal. , vol.24 , pp. 129-154
    • Rothe, F.1
  • 24
    • 51249171477 scopus 로고
    • On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields
    • Roussarie R. On the number of limit cycles which appear by perturbation of separatrix loop of planar vector fields. Bol. Soc. Brasil. Mat. 17 (1986) 67-101
    • (1986) Bol. Soc. Brasil. Mat. , vol.17 , pp. 67-101
    • Roussarie, R.1
  • 25
    • 0031508104 scopus 로고    scopus 로고
    • Local bifurcations of critical periods in the reduced Kukles system
    • Rousseau C., and Toni B. Local bifurcations of critical periods in the reduced Kukles system. Canad. J. Math. 49 (1997) 338-358
    • (1997) Canad. J. Math. , vol.49 , pp. 338-358
    • Rousseau, C.1    Toni, B.2
  • 26
    • 0041351881 scopus 로고    scopus 로고
    • Asymptotic expansion of the period function
    • Saavedra M. Asymptotic expansion of the period function. J. Differential Equations 193 (2003) 359-373
    • (2003) J. Differential Equations , vol.193 , pp. 359-373
    • Saavedra, M.1
  • 27
    • 3042708227 scopus 로고
    • Global behaviour of solution branches for some Neumann problems depending on one or several parameters
    • Schaaf R. Global behaviour of solution branches for some Neumann problems depending on one or several parameters. J. Reine Angew. Math. 346 (1984) 1-31
    • (1984) J. Reine Angew. Math. , vol.346 , pp. 1-31
    • Schaaf, R.1
  • 28
    • 0002499881 scopus 로고
    • A class of Hamiltonian systems with increasing periods
    • Schaaf R. A class of Hamiltonian systems with increasing periods. J. Reine Angew. Math. 363 (1985) 96-109
    • (1985) J. Reine Angew. Math. , vol.363 , pp. 96-109
    • Schaaf, R.1
  • 29
    • 0001304970 scopus 로고
    • Algebraic and geometric aspects of the theory of polynomial vector fields
    • Montreal, PQ, 1992, Kluwer Acad. Publ., Dordrecht
    • Schlomiuk D. Algebraic and geometric aspects of the theory of polynomial vector fields. Bifurcations and Periodic Orbits of Vector Fields. Montreal, PQ, 1992 (1993), Kluwer Acad. Publ., Dordrecht 429-467
    • (1993) Bifurcations and Periodic Orbits of Vector Fields , pp. 429-467
    • Schlomiuk, D.1
  • 30
    • 84968514049 scopus 로고
    • Algebraic particular integrals, integrability and the problem of the center
    • Schlomiuk D. Algebraic particular integrals, integrability and the problem of the center. Trans. Amer. Math. Soc. 338 (1993) 799-841
    • (1993) Trans. Amer. Math. Soc. , vol.338 , pp. 799-841
    • Schlomiuk, D.1
  • 31
    • 0000093987 scopus 로고
    • Global bifurcation of steady-state solutions
    • Smoller J., and Wasserman A. Global bifurcation of steady-state solutions. J. Differential Equations 39 (1981) 269-290
    • (1981) J. Differential Equations , vol.39 , pp. 269-290
    • Smoller, J.1    Wasserman, A.2
  • 32
    • 0022661610 scopus 로고
    • The period in the Lotka-Volterra system is monotonic
    • Waldvogel J. The period in the Lotka-Volterra system is monotonic. J. Math. Anal. Appl. 114 (1986) 178-184
    • (1986) J. Math. Anal. Appl. , vol.114 , pp. 178-184
    • Waldvogel, J.1
  • 33
    • 0035511438 scopus 로고    scopus 로고
    • Monotonicity criteria for an energy-period function in planar Hamiltonian systems
    • Zevin A.A., and Pinsky M.A. Monotonicity criteria for an energy-period function in planar Hamiltonian systems. Nonlinearity 14 (2001) 1425-1432
    • (2001) Nonlinearity , vol.14 , pp. 1425-1432
    • Zevin, A.A.1    Pinsky, M.A.2
  • 35
    • 10344255715 scopus 로고    scopus 로고
    • The period function for quadratic integrable systems with cubic orbits
    • Zhao Y. The period function for quadratic integrable systems with cubic orbits. J. Math. Anal. Appl. 301 (2005) 295-312
    • (2005) J. Math. Anal. Appl. , vol.301 , pp. 295-312
    • Zhao, Y.1
  • 36
    • 23844503727 scopus 로고    scopus 로고
    • On the monotonicity of the period function of a quadratic system
    • Zhao Y. On the monotonicity of the period function of a quadratic system. Discrete Contin. Dyn. Syst. 13 (2005) 795-810
    • (2005) Discrete Contin. Dyn. Syst. , vol.13 , pp. 795-810
    • Zhao, Y.1
  • 37
    • 0000813963 scopus 로고
    • Quadratic systems with center and their perturbations
    • Żoła̧dek H. Quadratic systems with center and their perturbations. J. Differential Equations 109 (1994) 223-273
    • (1994) J. Differential Equations , vol.109 , pp. 223-273
    • Zoła̧dek, H.1


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