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arXiv · 2304.12449

Feigenbaum scenario without parameters

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

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Ivan A. Korneev, Ibadulla R. Ramazanov, Andrei V. Slepnev, Tatiana E. Vadivasova, Vladimir V. Semenov. 2023-04-24. Feigenbaum scenario without parameters. https://arxiv.org/abs/2304.12449

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