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Crossover from dissipative to conservative behaviour in period-doubling systems

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  • Van Der Weele, J.P.
  • Capel, H.W.
  • Post, T.
  • Calkoen, Ch.J.

Abstract

We investigate the crossover properties, between the conservative and dissipative limit, for period-doubling bifurcations in two-dimentional iterative maps; as a generic example we use the standard form of the Hénon map. The approximants to the Feigenbaum constant δ lie on a universal crossover curve, which turns out to be non-monotonic. A similar curve is found for the scaling factor α. More generally, we discuss the crossover of the trajectory scaling function 1/ σ, and its properties in the conservative limit.

Suggested Citation

  • Van Der Weele, J.P. & Capel, H.W. & Post, T. & Calkoen, Ch.J., 1986. "Crossover from dissipative to conservative behaviour in period-doubling systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 137(1), pages 1-43.
    • Handle: RePEc:eee:phsmap:v:137:y:1986:i:1:p:1-43
    DOI: 10.1016/0378-4371(86)90062-2
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    References listed on IDEAS

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    1. Feigenbaum, Susan & Ortiz, Henry & Willett, Thomas D, 1985. "Protectionist Pressures and Aggregate Economic Conditions: Comment [Pressures for Protectionism: An Empirical Analysis]," Economic Inquiry, Western Economic Association International, vol. 23(1), pages 175-182, January.
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    2. Van Der Weele, J.P. & Capel, H.W., 1987. "The ƒ(a) formalism applied to the crossover from conservative to dissipative scaling behaviour in period doubling systems," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 147(1), pages 297-314.

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