Feigenbaum scenario without parameters

Ivan A Korneev; Ibadulla R Ramazanov; Andrei V Slepnev; Tatiana E Vadivasova; Vladimir V Semenov

doi:10.1063/5.0155982

Feigenbaum scenario without parameters

Chaos. 2023 Sep 1;33(9):091102. doi: 10.1063/5.0155982.

Authors

Ivan A Korneev¹, Ibadulla R Ramazanov¹, Andrei V Slepnev¹, Tatiana E Vadivasova¹, Vladimir V Semenov¹

Affiliation

¹ Institute of Physics, Saratov State University, Astrakhanskaya str. 83, 410012 Saratov, Russia.

PMID: 37682031
DOI: 10.1063/5.0155982

Abstract

Typically, the period-doubling bifurcations exhibited by nonlinear dissipative systems are observed when varying systems' parameters. In contrast, the period-doubling bifurcations considered in the current research are induced by changing the initial conditions, whereas parameter values are fixed. Thus, the studied bifurcations can be classified as the period-doubling bifurcations without parameters. Moreover, we show a cascade of the period-doubling bifurcations without parameters, resulting in a transition to deterministic chaos. The explored effects are demonstrated by means of numerical modeling on an example of a modified Anishchenko-Astakhov self-oscillator where the ability to exhibit bifurcations without parameters is associated with the properties of a memristor. Finally, we compare the dynamics of the ideal-memristor-based oscillator with the behavior of a model taking into account the memristor forgetting effect.