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Change of structure and chaos for solutions of \(\dot x\)(t) = −f(x(t−1))

Part of the Lecture Notes in Mathematics book series (LNM,volume 878)

Keywords

  • Periodic Solution
  • Initial Function
  • Shift Operator
  • Homoclinic Solution
  • Strict Feedback

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VI. References

  1. M.J. Feigenbaum, Quantitative universality for a class of nonlinear transformations, J.Stat.Phys. 19, 1978, 25–52

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  2. T. Furumochi, Existence of periodic solutions of one-dimensional differential-delay equations, Tôhoku Math.J. 30, 1978, 13–35

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  3. T.Y. Li-J.A. Yorke, Period three implies chaos, Am.Math.Monthly 82, 1975, 985–992

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  4. R.D. Nussbaum, Periodic solutions of nonlinear autonomous functional differential equations, in "Functional Differential Equations and Approximation of Fixed Points", Springer Lecture Notes in Math. 730, 1979, 283–326

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  5. R.D. Nussbaum, Uniqueness and nonuniqueness for periodic solutions of x′(t)=−g(x(t−1)), J.Diff.Eq. 34, 1979, 25–54

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  6. R.D. Nussbaum-H.-O. Peitgen, Spurious and special periodic solutions of \(\dot x\)(t)=−λf(x(t−1)), to appear

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  7. H. Peters, Comportement chaotique d'une équation différentielle retardée, C.R.Acad.Sci. Paris 290, 1980, 1119–1122

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  8. H.W. Siegberg, PhD-thesis, Bremen 1981

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© 1981 Springer-Verlag

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Peters, H. (1981). Change of structure and chaos for solutions of \(\dot x\)(t) = −f(x(t−1)). In: Allgower, E.L., Glashoff, K., Peitgen, HO. (eds) Numerical Solution of Nonlinear Equations. Lecture Notes in Mathematics, vol 878. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0090687

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  • DOI: https://doi.org/10.1007/BFb0090687

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