Extreme multistability and antimonotonicity in a Shinriki oscillator with two flux-controlled memristors. (English) Zbl 1478.34060
Summary: This paper proposes a novel memristive chaotic circuit which originated from a Shinriki oscillator with two flux-controlled memristors of different polarities. This two-memristor-based Shinriki oscillator (TMSO) having a special plane equilibrium is prone to exhibiting the initial-dependent phenomenon of extreme multistability. To investigate its internal dynamics, a third-order dimensionality reduction model is established by utilizing the constitutive relationship of its memristor’s flux and charge. The uncertain plane equilibrium is transfered into some deterministic model that can accurately predict the dynamical evolution of the system, where interesting phenomena of asymmetric bifurcations, extreme multistability and antimonotonicity are detected and analyzed by evaluating the position and stability of the equilibria in the flux-charge model. The simulation is carried out via Multisim to validate the analysis model, and the comparison of the phase trajectories, before and after dimensionality reduction, shows that this oscillator is good for research and practical use.
MSC:
| 34C60 | Qualitative investigation and simulation of ordinary differential equation models |
| 94C60 | Circuits in qualitative investigation and simulation of models |
| 34C05 | Topological structure of integral curves, singular points, limit cycles of ordinary differential equations |
| 34D20 | Stability of solutions to ordinary differential equations |
| 34C23 | Bifurcation theory for ordinary differential equations |
| 34C28 | Complex behavior and chaotic systems of ordinary differential equations |
| 34C20 | Transformation and reduction of ordinary differential equations and systems, normal forms |
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