Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system
Nowadays, multistability assessment in discrete nonlinear fractional difference systems is an emotive topic. This paper introduces a novel discrete, nonequilibrium, memristor-based Hindmarsh–Rose neuron (HRN) with the Caputo fractional difference scheme. Furthermore, in a setting involving commensur...
| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Elsevier
2023-08-01
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| Series: | Results in Physics |
| Subjects: | |
| Online Access: | http://www.sciencedirect.com/science/article/pii/S2211379723004205 |
| _version_ | 1797755000357650432 |
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| author | Maysaa Al-Qurashi Qurat Ul Ain Asif Yu-Ming Chu Saima Rashid S.K. Elagan |
| author_facet | Maysaa Al-Qurashi Qurat Ul Ain Asif Yu-Ming Chu Saima Rashid S.K. Elagan |
| author_sort | Maysaa Al-Qurashi |
| collection | DOAJ |
| description | Nowadays, multistability assessment in discrete nonlinear fractional difference systems is an emotive topic. This paper introduces a novel discrete, nonequilibrium, memristor-based Hindmarsh–Rose neuron (HRN) with the Caputo fractional difference scheme. Furthermore, in a setting involving commensurate and incommensurate scenarios, the complex structure of the proposed discrete fractional model, which includes its multistability, concealed chaos and hyperchaotic attractor, is examined using a wide range of computational approaches, such as Lyapunov exponents, phase portraits, bifurcation illustrations, and the 0–1 evaluation emergence of synchronization. These evolving properties imply that the fractional discrete HRN has an undetected multistability. Ultimately, an elaborate investigation is performed to confirm the existence of unpredictability employing approximation entropy (ApEn) and the ℂ0 measurements. It is demonstrated that whenever the immediate synchronization indicates that it happens, the neurons’ interactions modify, recurring in decreasing fractional orders. Furthermore, minimizing the derivative order increases the incidence of explosions in the synchronization manifold, which is opposite to the behaviour of one nerve cell. |
| first_indexed | 2024-03-12T17:41:36Z |
| format | Article |
| id | doaj.art-545b2d68034643c59b39b3c9f5d24407 |
| institution | Directory Open Access Journal |
| issn | 2211-3797 |
| language | English |
| last_indexed | 2024-03-12T17:41:36Z |
| publishDate | 2023-08-01 |
| publisher | Elsevier |
| record_format | Article |
| series | Results in Physics |
| spelling | doaj.art-545b2d68034643c59b39b3c9f5d244072023-08-04T05:47:03ZengElsevierResults in Physics2211-37972023-08-0151106627Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron systemMaysaa Al-Qurashi0Qurat Ul Ain Asif1Yu-Ming Chu2Saima Rashid3S.K. Elagan4Department of Mathematics, King Saud University, P.O. Box 22452, Riyadh 11495, Saudi Arabia; Department of Mathematics, Saudi Electronic University, Riyadh, Saudi ArabiaDepartment of Physics, Government College University, Faisalabad 38000, PakistanDepartment of Mathematics, Huzhou University, Huzhou, 313000, China; Corresponding authors.Department of Mathematics, Government College University, Faisalabad 38000, Pakistan; Corresponding authors.Department of Mathematics and Statistics, College of Science, Taif University, P.O. Box 11099, Taif 21944, Saudi ArabiaNowadays, multistability assessment in discrete nonlinear fractional difference systems is an emotive topic. This paper introduces a novel discrete, nonequilibrium, memristor-based Hindmarsh–Rose neuron (HRN) with the Caputo fractional difference scheme. Furthermore, in a setting involving commensurate and incommensurate scenarios, the complex structure of the proposed discrete fractional model, which includes its multistability, concealed chaos and hyperchaotic attractor, is examined using a wide range of computational approaches, such as Lyapunov exponents, phase portraits, bifurcation illustrations, and the 0–1 evaluation emergence of synchronization. These evolving properties imply that the fractional discrete HRN has an undetected multistability. Ultimately, an elaborate investigation is performed to confirm the existence of unpredictability employing approximation entropy (ApEn) and the ℂ0 measurements. It is demonstrated that whenever the immediate synchronization indicates that it happens, the neurons’ interactions modify, recurring in decreasing fractional orders. Furthermore, minimizing the derivative order increases the incidence of explosions in the synchronization manifold, which is opposite to the behaviour of one nerve cell.http://www.sciencedirect.com/science/article/pii/S2211379723004205Hindmarsh–Rose neuron modelCaputo fractional difference operatorLyapunov exponentsBifurcation illustrationsDegree of complexity |
| spellingShingle | Maysaa Al-Qurashi Qurat Ul Ain Asif Yu-Ming Chu Saima Rashid S.K. Elagan Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system Results in Physics Hindmarsh–Rose neuron model Caputo fractional difference operator Lyapunov exponents Bifurcation illustrations Degree of complexity |
| title | Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system |
| title_full | Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system |
| title_fullStr | Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system |
| title_full_unstemmed | Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system |
| title_short | Complexity analysis and discrete fractional difference implementation of the Hindmarsh–Rose neuron system |
| title_sort | complexity analysis and discrete fractional difference implementation of the hindmarsh rose neuron system |
| topic | Hindmarsh–Rose neuron model Caputo fractional difference operator Lyapunov exponents Bifurcation illustrations Degree of complexity |
| url | http://www.sciencedirect.com/science/article/pii/S2211379723004205 |
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