Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns
Fractional nonlinear systems have been considered in many fields due to their ability to bring memory-dependent properties into various systems. Therefore, using fractional derivatives to model real-world phenomena, such as neuronal dynamics, is of significant importance. This paper presents the fra...
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| Format: | Article |
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MDPI AG
2022-08-01
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| Series: | Mathematics |
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| Online Access: | https://www.mdpi.com/2227-7390/10/16/2827 |
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| author | Gayathri Vivekanandan Mahtab Mehrabbeik Hayder Natiq Karthikeyan Rajagopal Esteban Tlelo-Cuautle |
| author_facet | Gayathri Vivekanandan Mahtab Mehrabbeik Hayder Natiq Karthikeyan Rajagopal Esteban Tlelo-Cuautle |
| author_sort | Gayathri Vivekanandan |
| collection | DOAJ |
| description | Fractional nonlinear systems have been considered in many fields due to their ability to bring memory-dependent properties into various systems. Therefore, using fractional derivatives to model real-world phenomena, such as neuronal dynamics, is of significant importance. This paper presents the fractional memristive Wilson neuron model and studies its dynamics as a single neuron. Furthermore, the collective behavior of neurons is researched when they are locally and diffusively coupled in a ring topology. It is found that the fractional-order neurons are bistable in some values of the fractional order. Additionally, complete synchronization, lag synchronization, phase synchronization, and sine-like synchronization patterns can be observed in the constructed network with different fractional orders. |
| first_indexed | 2024-03-09T04:09:11Z |
| format | Article |
| id | doaj.art-ed771851ce5b4e30af9b8567a5861eef |
| institution | Directory Open Access Journal |
| issn | 2227-7390 |
| language | English |
| last_indexed | 2024-03-09T04:09:11Z |
| publishDate | 2022-08-01 |
| publisher | MDPI AG |
| record_format | Article |
| series | Mathematics |
| spelling | doaj.art-ed771851ce5b4e30af9b8567a5861eef2023-12-03T14:02:51ZengMDPI AGMathematics2227-73902022-08-011016282710.3390/math10162827Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization PatternsGayathri Vivekanandan0Mahtab Mehrabbeik1Hayder Natiq2Karthikeyan Rajagopal3Esteban Tlelo-Cuautle4Centre for Artificial Intelligence, Chennai Institute of Technology, Chennai 600069, IndiaDepartment of Biomedical Engineering, Amirkabir University of Technology (Tehran Polytechnic), Tehran 159163-4311, IranInformation Technology Collage, Imam Ja’afar Al-Sadiq University, Baghdad 10001, IraqCentre for Nonlinear Systems, Chennai Institute of Technology, Chennai 600069, IndiaINAOE, Department of Electronics, Luis Enrique Erro No.1, Santa María Tonanzintla, San Andrés Cholula, Puebla 72840, MexicoFractional nonlinear systems have been considered in many fields due to their ability to bring memory-dependent properties into various systems. Therefore, using fractional derivatives to model real-world phenomena, such as neuronal dynamics, is of significant importance. This paper presents the fractional memristive Wilson neuron model and studies its dynamics as a single neuron. Furthermore, the collective behavior of neurons is researched when they are locally and diffusively coupled in a ring topology. It is found that the fractional-order neurons are bistable in some values of the fractional order. Additionally, complete synchronization, lag synchronization, phase synchronization, and sine-like synchronization patterns can be observed in the constructed network with different fractional orders.https://www.mdpi.com/2227-7390/10/16/2827fractional-order derivativememristive Wilson modelsynchronizationmultistability |
| spellingShingle | Gayathri Vivekanandan Mahtab Mehrabbeik Hayder Natiq Karthikeyan Rajagopal Esteban Tlelo-Cuautle Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns Mathematics fractional-order derivative memristive Wilson model synchronization multistability |
| title | Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns |
| title_full | Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns |
| title_fullStr | Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns |
| title_full_unstemmed | Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns |
| title_short | Fractional-Order Memristive Wilson Neuron Model: Dynamical Analysis and Synchronization Patterns |
| title_sort | fractional order memristive wilson neuron model dynamical analysis and synchronization patterns |
| topic | fractional-order derivative memristive Wilson model synchronization multistability |
| url | https://www.mdpi.com/2227-7390/10/16/2827 |
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