https://doi.org/10.1140/epjp/s13360-022-02779-4
Regular Article
Approximate symmetry memristive mega-stable oscillator with attractor growing and its Hamilton energy balance
1
Centre for Nonlinear Systems, Chennai Institute of Technology, Chennai, India
2
Information Technology Collage, Imam Ja’afar Al-Sadiq University, 10001, Baghdad, Iraq
3
Health Technology Research Institute, Amirkabir University of Technology, 424 Hafez Ave., 15875-4413, Tehran, Iran
4
Department of Biomedical Engineering, Amirkabir University of Technology, 424 Hafez Ave., 15875-4413, Tehran, Iran
5
National Higher Polytechnic Institute (NAHPI), University of Bamenda, P.O. Box 39, Bambili North West Region, Cameroon
6
Department of Electrical Engineering, École de Technologie Supérieure (ÉTS), H3C1K3, Montréal, Québec, Canada
Received:
28
December
2021
Accepted:
28
April
2022
Published online:
16
May
2022
A unique mega-stable oscillator with a memristor device is constructed, with the special properties of parity invariant, approximate symmetry, and attractor growing. The introduced memristor device with sinusoidal functions holds the polarity when each variable switches from positive to negative, and correspondingly approximate symmetric coexisting quasi-periodic attractors are coined. More importantly, with the two periodic functions, the new memristive mega-stable oscillator originates the remarkable phenomenon of attractor growing with an infinite number of coexisting attractors. Such behaviors are investigated by using phase portraits, Poincaré section, and time series. The Hamilton energy balance based on Helmholtz’s theorem explains the dependence of the initial conditions on the mega-stability mechanism. Moreover, we show how the isosurface for which this Hamilton energy is a constant strongly depends on state variables.
© The Author(s), under exclusive licence to Società Italiana di Fisica and Springer-Verlag GmbH Germany, part of Springer Nature 2022
