Convergence rates for sequences of bifurcation parameters of nonautonomous dynamical systems generated by flat top tent maps
| Autor: | Teresa Morais Silva, Luís Silva, Sara Fernandes |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2020 |
| Předmět: |
Period-doubling bifurcation
Numerical Analysis Mathematics::Dynamical Systems Rates of convergence Dynamical systems theory Applied Mathematics Stunted tent maps Symbolic dynamics Star (graph theory) Parameter space 01 natural sciences 010305 fluids & plasmas Star product Modeling and Simulation 0103 physical sciences Convergence (routing) Applied mathematics 010306 general physics Nonautonomous periodic systems Bifurcation Mathematics |
| Zdroj: | Repositório Científico de Acesso Aberto de Portugal Repositório Científico de Acesso Aberto de Portugal (RCAAP) instacron:RCAAP |
| Popis: | In this paper we study a 2-parameter family of 2-periodic nonautonomous systems generated by the alternate iteration of two stunted tent maps. Using symbolic dynamics, renormalization and star product in the nonautonomous setting, we compute the convergence rates of sequences of parameters obtained through consecutive star products/renormalizations, extending in this way Feigenbaum’s convergence rates. We also define sequences in the parameter space corresponding to anharmonic period doubling bifurcations and compute their convergence rates. In both cases we show that the convergence rates are independent of the initial point, concluding that the nonautonomous setting has universal properties of the type found by Feigenbaum in families of autonomous systems. |
| Databáze: | OpenAIRE |
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