Dynamical properties of a small heterogeneous chain network of neurons in discrete time
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arXiv
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| Auteurs principaux: | , , , |
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| Format: | Preprint |
| Publié: |
2024
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| _version_ | 1866929340420194304 |
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| author | Ghosh, Indranil Nair, Anjana S. Fatoyinbo, Hammed Olawale Muni, Sishu Shankar |
| author_facet | Ghosh, Indranil Nair, Anjana S. Fatoyinbo, Hammed Olawale Muni, Sishu Shankar |
| contents | We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2405_05675 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Dynamical properties of a small heterogeneous chain network of neurons in discrete time Ghosh, Indranil Nair, Anjana S. Fatoyinbo, Hammed Olawale Muni, Sishu Shankar Adaptation and Self-Organizing Systems Chaotic Dynamics We propose a novel nonlinear bidirectionally coupled heterogeneous chain network whose dynamics evolve in discrete time. The backbone of the model is a pair of popular map-based neuron models, the Chialvo and the Rulkov maps. This model is assumed to proximate the intricate dynamical properties of neurons in the widely complex nervous system. The model is first realized via various nonlinear analysis techniques: fixed point analysis, phase portraits, Jacobian matrix, and bifurcation diagrams. We observe the coexistence of chaotic and period-4 attractors. Various codimension-1 and -2 patterns for example saddle-node, period-doubling, Neimark-Sacker, double Neimark-Sacker, flip- and fold-Neimark Sacker, and 1:1 and 1:2 resonance are also explored. Furthermore, the study employs two synchronization measures to quantify how the oscillators in the network behave in tandem with each other over a long number of iterations. Finally, a time series analysis of the model is performed to investigate its complexity in terms of sample entropy. |
| title | Dynamical properties of a small heterogeneous chain network of neurons in discrete time |
| topic | Adaptation and Self-Organizing Systems Chaotic Dynamics |
| url | https://arxiv.org/abs/2405.05675 |