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Exchange of stability along a branch of periodic solutions of a single specie model

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Part of the Lecture Notes in Mathematics book series (LNM,volume 1017)

Keywords

  • Periodic Solution
  • Functional Differential Equation
  • Positive Equilibrium
  • Positive Periodic Solution
  • Ordinary Case

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References

  1. Badii, M., Schiaffino, A.: Asymptotic behaviour of positive solutions of periodic delay logistic equations. J.Math.Biol. 14, 95–100 (1982)

    CrossRef  MathSciNet  MATH  Google Scholar 

  2. Bardi,M.: An equation of growth of a single specie with realistic dependence on crowding and seasonal factors. Preprint

    Google Scholar 

  3. Bardi,M.: A nonautonomous nonlinear functional differential equation arising in the theory of population dynamics. Preprint

    Google Scholar 

  4. Clark, C.W.: Mathematical bioeconomics: the optimal management of renewable resources. New York: Wiley 1976

    MATH  Google Scholar 

  5. Crandall, M.G., Rabinowitz, P.H.: Bifurcation, perturbation of simple eigenvalues, and linearized stability. Arch.Rat.Mech.Anal. 52, 161–180 (1973)

    CrossRef  MathSciNet  MATH  Google Scholar 

  6. Cushing, J.M.: Stable positive periodic solutions of the time-dependent logistic equation under possible hereditary influences. J.Math.Anal.Appl. 60, 747–754 (1977)

    CrossRef  MathSciNet  MATH  Google Scholar 

  7. de Mottoni, P., Schiaffino, A.: Bifurcation of periodic solutions for some systems with periodic coefficients. In: Nonlinear differential equations (P. de Mottoni and L. Salvadori, eds.), pp.327–338. New York: Academic Press 1981

    CrossRef  Google Scholar 

  8. de Mottoni, P., Schiaffino, A.: Competition systems with periodic coefficients: a geometric approach. J.Math.Biol. 11, 319–335 (1981)

    CrossRef  MathSciNet  MATH  Google Scholar 

  9. Iooss, G., Joseph, D.D.: Elementary stability and bifurcation theory. New York: Springer Verlag 1980

    CrossRef  MATH  Google Scholar 

  10. Joseph, D.D.: Factorization theorems, stability, and repeated bifurcation. Arch.Rat.Mech.Anal. 66, 99–118 (1977)

    MathSciNet  MATH  Google Scholar 

  11. Joseph, D.D.: Factorization theorems and repeated branching of solutions at a simple eigenvalue. Ann.New York Acad.Sci. 316, 150–167 (1979)

    CrossRef  MathSciNet  Google Scholar 

  12. Joseph, D.D., Nield, D.A.: Stability of bifurcating time-periodic and steady solutions of arbitrary amplitude. Arch.Rat.Mech.Anal. 58, 369–380 (1975)

    CrossRef  MathSciNet  MATH  Google Scholar 

  13. Krasnosel'skii, M.A.: The theory of periodic solutions of non-autonomous differential equations. Russian Math.Surveys 21, 53–74 (1966)

    CrossRef  MathSciNet  Google Scholar 

  14. Rosenblat, S.: Global aspects of bifurcation and stability. Arch.Rat.Mech.Anal. 66, 119–134 (1977)

    CrossRef  MathSciNet  MATH  Google Scholar 

  15. Sattinger, D.H.: Stability of solutions of nonlinear equations. J. Math.Anal.Appl. 39, 1–12 (1972)

    CrossRef  MathSciNet  MATH  Google Scholar 

  16. Weinberger, H.F.: The stability of solutions bifurcating from steady or periodic solutions. Univ.Florida Internat.Symp.Dynamical Systems. New York: Academic Press 1977

    Google Scholar 

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© 1983 Springer-Verlag

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Bardi, M. (1983). Exchange of stability along a branch of periodic solutions of a single specie model. In: Knobloch, H.W., Schmitt, K. (eds) Equadiff 82. Lecture Notes in Mathematics, vol 1017. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0103237

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  • DOI: https://doi.org/10.1007/BFb0103237

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  • Publisher Name: Springer, Berlin, Heidelberg

  • Print ISBN: 978-3-540-12686-7

  • Online ISBN: 978-3-540-38678-0

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