On some elliptic generalizations of the Metropolis–Stein–Stein map

Chacón, Ricardo ; Martínez, Pedro J. (Universidad de Zaragoza)

Resumen: Jacobian elliptic functions have been at the heart of nonlinear science for two hundred years. Through the exploration of two biparametric (,) elliptic-based generalizations of the Metropolis–Stein–Stein (MSS) map, +1 = sn() and +1 = sncn(), with sn and cn being Jacobian elliptic functions of parameter , we provide analytical and numerical evidence that solely varying the impulse per unit of amplitude of the periodic map functions, while keeping its amplitude constant, shifts the bifurcation amplitudes, including those corresponding to the onset and extinction of chaos, with respect to the case of the standard MSS map. The analyses of the Schwarzian derivative of the two elliptic maps indicate that a change of its sign from negative to positive as the shape parameter is increased from 0 to 1 only occurs for the map sncn, while the corresponding routes order↔chaos for both elliptic maps still follow Feigenbaum’s universality. We found that maximal extension of the state space wherein sncn presents a positive Schwarzian derivative occurs at a single critical value of the shape parameter: = ≃ 0.985682. Remarkably, this value corresponds to a magic universal waveform which optimally enhances directed ratchet transport by symmetry breaking and is associated with an enhancement of chaos for ≲ 1 in parameter space with respect to the shift-symmetric map sn It should be emphasized that this change in the sign of the Schwarzian derivative is a genuine feature of the map sncn which is completely absent in the standard MSS map

Idioma: Inglés

DOI: 10.1016/j.physd.2025.135036

Año: 2025

Publicado en: PHYSICA D-NONLINEAR PHENOMENA 484 (2025), 135036 [8 p.]
ISSN: 0167-2789

Financiación: info:eu-repo/grantAgreement/ES/DGA/E36-23R
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2019-108508GB-I00
Financiación: info:eu-repo/grantAgreement/ES/MICINN/PID2023-147734NB-I00

Tipo y forma: Artículo (PrePrint)

Área (Departamento): Área Física Aplicada (Dpto. Física Aplicada)