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Attractors in Pattern Iterations of Flat Top Tent Maps

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  • Luis Silva

    (CIMA and Department of Mathematics of ISEL-Higher Institute of Engineering of Lisbon, Rua Conselheiro Emídio Navarro, 1, 1959-007 Lisbon, Portugal)

Abstract

Flat-topped one-dimensional maps have been used in the control of chaos in one-dimensional dynamical systems. In these applications, this mechanism is known as simple limiter control. In this paper, we will consider the introduction of simple limiters u in the tent map, according to a time-dependent scheme defined by a binary sequence s , the iteration pattern. We will define local and Milnor attractors in this non-autonomous context and study the dependence of their existence and coexistence on the value of the limiter u and on the pattern s . Using symbolic dynamics, we will be able to characterize the families of pairs ( u , s ) for which these attractors exist and coexist, as well as fully describe them. We will observe that this non-autonomous context provides a richness of behaviors that are not possible in the autonomous case.

Suggested Citation

  • Luis Silva, 2023. "Attractors in Pattern Iterations of Flat Top Tent Maps," Mathematics, MDPI, vol. 11(12), pages 1-13, June.
    • Handle: RePEc:gam:jmathe:v:11:y:2023:i:12:p:2677-:d:1169767
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    References listed on IDEAS

    as
    1. He, Xue-Zhong & Westerhoff, Frank H., 2005. "Commodity markets, price limiters and speculative price dynamics," Journal of Economic Dynamics and Control, Elsevier, vol. 29(9), pages 1577-1596, September.
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