Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation
In this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal...
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| Format: | Article |
| Language: | English |
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Akif AKGUL
2022-11-01
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| Series: | Chaos Theory and Applications |
| Subjects: | |
| Online Access: | https://dergipark.org.tr/en/download/article-file/2539611 |
| _version_ | 1827341612989022208 |
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| author | Jan Awrejcewicz Théophile Fozin Cyrille Feudjio Sishu Shankar Muni Zeric Njıtacke |
| author_facet | Jan Awrejcewicz Théophile Fozin Cyrille Feudjio Sishu Shankar Muni Zeric Njıtacke |
| author_sort | Jan Awrejcewicz |
| collection | DOAJ |
| description | In this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent , chimera and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a differet state where there is a coexistence of synchroniaed and asynchronized nodes of the network. One of the interesting result of the paper is the prevalence of double-well chimera states in both ring and ring-star network and has been first mentioned in the case of memrisitve HR neuron model. |
| first_indexed | 2024-03-07T21:45:31Z |
| format | Article |
| id | doaj.art-89a044d6c41142c08063dc8663134f84 |
| institution | Directory Open Access Journal |
| issn | 2687-4539 |
| language | English |
| last_indexed | 2024-03-07T21:45:31Z |
| publishDate | 2022-11-01 |
| publisher | Akif AKGUL |
| record_format | Article |
| series | Chaos Theory and Applications |
| spelling | doaj.art-89a044d6c41142c08063dc8663134f842024-02-25T19:10:00ZengAkif AKGULChaos Theory and Applications2687-45392022-11-014311912710.51537/chaos.11441231971Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External ExcitationJan Awrejcewicz0Théophile Fozin1Cyrille Feudjio2Sishu Shankar Muni3Zeric Njıtacke4Lodz University of technologyUniversity of BueaUniversity of BueaMassey UniversityUniversity of BueaIn this paper we have introduced and investigated the collective behavior of a network of memristive Hindmarsh-Rose (HR) neurons. The proposed model was built considering the memristive autapse of the traditional 2D HR neuron. Using the one-parameter bifurcation diagram and its corresponding maximal Lyapunov exponent graph, we showed that the proposed model was able to exhibit a reverse period doubling route to chaos, phenomenon of interior and exterior crises. Three different configurations of the ring-star network of the memristive HR neuron model, including ring-star, ring, and star, have been considered. The study of those network configurations revealed incoherent, coherent , chimera and cluster state behaviors. Coherent behavior is characterized by synchronization of the neurons of the network, while incoherent behaviors are characterized by the absence of synchronization. Chimera states refer to a differet state where there is a coexistence of synchroniaed and asynchronized nodes of the network. One of the interesting result of the paper is the prevalence of double-well chimera states in both ring and ring-star network and has been first mentioned in the case of memrisitve HR neuron model.https://dergipark.org.tr/en/download/article-file/25396112d hindmarsh- rose neuronmemristive autapse routes to chaosring-star networkchimera statesdouble-well chimera state |
| spellingShingle | Jan Awrejcewicz Théophile Fozin Cyrille Feudjio Sishu Shankar Muni Zeric Njıtacke Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation Chaos Theory and Applications 2d hindmarsh- rose neuron memristive autapse routes to chaos ring-star network chimera states double-well chimera state |
| title | Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation |
| title_full | Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation |
| title_fullStr | Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation |
| title_full_unstemmed | Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation |
| title_short | Route to Chaos and Chimera States in a Network of Memristive Hindmarsh-Rose Neurons Model with External Excitation |
| title_sort | route to chaos and chimera states in a network of memristive hindmarsh rose neurons model with external excitation |
| topic | 2d hindmarsh- rose neuron memristive autapse routes to chaos ring-star network chimera states double-well chimera state |
| url | https://dergipark.org.tr/en/download/article-file/2539611 |
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