Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities
The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wi...
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| Format: | Article |
| Language: | English |
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MDPI AG
2024-01-01
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| Series: | Entropy |
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| Online Access: | https://www.mdpi.com/1099-4300/26/2/115 |
| _version_ | 1797298335260868608 |
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| author | Adrian-Mihail Stoica Isaac Yaesh |
| author_facet | Adrian-Mihail Stoica Isaac Yaesh |
| author_sort | Adrian-Mihail Stoica |
| collection | DOAJ |
| description | The paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wide neural network of a single hidden layer, such as the error equation of Hopfield networks with respect to equilibria or visuo-motor tasks. It is shown that driving such systems with a certain amount of state-multiplicative noise, one can stabilize noise-free unstable systems. Linear-Matrix-Inequality-based stabilization conditions are derived, utilizing a novel non-quadratic Lyapunov functional and a numerical example where state-multiplicative noise stabilizes a nonlinear system exhibiting chaotic behavior is demonstrated. |
| first_indexed | 2024-03-07T22:33:27Z |
| format | Article |
| id | doaj.art-42c8c2978d1d4235afd00273d6111bf2 |
| institution | Directory Open Access Journal |
| issn | 1099-4300 |
| language | English |
| last_indexed | 2024-03-07T22:33:27Z |
| publishDate | 2024-01-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Entropy |
| spelling | doaj.art-42c8c2978d1d4235afd00273d6111bf22024-02-23T15:15:38ZengMDPI AGEntropy1099-43002024-01-0126211510.3390/e26020115Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type NonlinearitiesAdrian-Mihail Stoica0Isaac Yaesh1Faculty of Aerospace Engineering, University Politehnica of Bucharest, 060042 Bucharest, RomaniaControl Department, Elbit Systems, Ramat-Hasharon 3100401, IsraelThe paradigm of stochastic antiresonance is considered for a class of nonlinear systems with sector bounded nonlinearities. Such systems arise in a variety of situations such as in engineering applications, in physics, in biology, and in systems with more general nonlinearities, approximated by a wide neural network of a single hidden layer, such as the error equation of Hopfield networks with respect to equilibria or visuo-motor tasks. It is shown that driving such systems with a certain amount of state-multiplicative noise, one can stabilize noise-free unstable systems. Linear-Matrix-Inequality-based stabilization conditions are derived, utilizing a novel non-quadratic Lyapunov functional and a numerical example where state-multiplicative noise stabilizes a nonlinear system exhibiting chaotic behavior is demonstrated.https://www.mdpi.com/1099-4300/26/2/115stochastic antiresonancesector-bounded nonlinearitiesstochastic systems with state- dependent noisestability analysisinfinitesimal generator |
| spellingShingle | Adrian-Mihail Stoica Isaac Yaesh Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities Entropy stochastic antiresonance sector-bounded nonlinearities stochastic systems with state- dependent noise stability analysis infinitesimal generator |
| title | Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities |
| title_full | Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities |
| title_fullStr | Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities |
| title_full_unstemmed | Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities |
| title_short | Stochastic Antiresonance for Systems with Multiplicative Noise and Sector-Type Nonlinearities |
| title_sort | stochastic antiresonance for systems with multiplicative noise and sector type nonlinearities |
| topic | stochastic antiresonance sector-bounded nonlinearities stochastic systems with state- dependent noise stability analysis infinitesimal generator |
| url | https://www.mdpi.com/1099-4300/26/2/115 |
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