https://doi.org/10.1140/epjs/s11734-024-01406-w
Regular Article
Dynamical analysis of non-electric guitar-like instruments with single saddle via Hopf bifurcation
Department of Mathematics, The Gandhigram Rural Institute (Deemed to be University), 624 302, Gandhigram, Tamil Nadu, India
Received:
3
May
2024
Accepted:
14
November
2024
Published online:
2
December
2024
In this work, the string network of non-electric n-stringed guitar-like instruments with a single bridge saddle is modeled based on the standard model of bidirectional associative memory (BAM) neural networks. These kinds of instruments play a lead role in many orchestras. Hence, the approximation of the accuracy of sound is more important. To attain accuracy, instead of considering an integer order system, we scrutinize the fractional order system of the proposed model with leakage and communication delays. Then, Hopf bifurcation is analyzed for the proposed fractional ordered delayed system. Also, Hopf bifurcation anti-control is investigated for the same system because an anti-controlled system is more efficient than a non-anti-controlled stable system. Finally, the stability switching region is derived. Moreover, the viability of the obtained theoretical results is verified for real-time four-stringed guitar model.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2024
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
