Feigenbaum scenario without parameters
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 transition to deterministic chaos. The explored effects are demonstrated by means of numerical modelling 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 behaviour of a model taking into account the memristor forgetting effect.
Keywords
Cite
@article{arxiv.2304.12449,
title = {Feigenbaum scenario without parameters},
author = {Ivan A. Korneev and Ibadulla R. Ramazanov and Andrei V. Slepnev and Tatiana E. Vadivasova and Vladimir V. Semenov},
journal= {arXiv preprint arXiv:2304.12449},
year = {2023}
}
Comments
9 pages, 5 figures