Abstract
This report investigates the stability problem of memristive systems with a line of equilibria on the example of SBT memristor-based Wien-bridge circuit. For the considered system, conditions of local and global partial stability are obtained, and chaotic dynamics is studied.
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For any \(\varepsilon > 0\) there exists \(\delta > 0\), such that, if \(|u(0) - u_{eq}| < \delta \), then \(|u(t) - u_{eq}| < \varepsilon \) is valid for all \(t > 0\). Recall that local asymptotic stability of \(u_{eq}\) means that \(u_{eq}\) is locally Lyapunov stable and also there exists \(\delta > 0\), such that if \(|u(0) - u_{eq}| < \delta \), then \(\lim _{t \rightarrow \infty } |u(t) - u_{eq}| = 0\). Thus, due to the noise, the state of the physical model may drift along the line of equilibria.
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Acknowledgements
The authors wish to thank Prof. Leon Chua (University of California, Berkeley, USA) for the fruitful discussions and valuable comments on memristive systems. This work was supported by Russian Scientific Foundation project 19-41-02002 (Sects. 2–4) the Leading Scientific Schools of Russia grant NSh-2858.2018.1 (Sect. 1).
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Kuznetsov, N.V. et al. (2020). Stability and Chaotic Attractors of Memristor-Based Circuit with a Line of Equilibria. In: Zelinka, I., Brandstetter, P., Trong Dao, T., Hoang Duy, V., Kim, S. (eds) AETA 2018 - Recent Advances in Electrical Engineering and Related Sciences: Theory and Application. AETA 2018. Lecture Notes in Electrical Engineering, vol 554. Springer, Cham. https://doi.org/10.1007/978-3-030-14907-9_62
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