Mean-field approximation for networks with synchrony-driven adaptive coupling
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arXiv
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| Autores principales: | , , , , |
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| Formato: | Preprint |
| Publicado: |
2024
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| _version_ | 1866911973642338304 |
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| author | Fennelly, Niamh Neff, Alannah Lambiotte, Renaud Keane, Andrew Byrne, Áine |
| author_facet | Fennelly, Niamh Neff, Alannah Lambiotte, Renaud Keane, Andrew Byrne, Áine |
| contents | Synaptic plasticity is a key component of neuronal dynamics, describing the process by which the connections between neurons change in response to experiences. In this study, we extend a network model of $θ$-neuron oscillators to include a realistic form of adaptive plasticity. In place of the less tractable spike-timing-dependent plasticity, we employ recently validated phase-difference-dependent plasticity rules, which adjust coupling strengths based on the relative phases of $θ$-neuron oscillators. We investigate two approaches for implementing this plasticity: pairwise coupling strength updates and global coupling strength updates. A mean-field approximation of the system is derived and we investigate its validity through comparison with the $θ$-neuron simulations across various stability states. The synchrony of the system is examined using the Kuramoto order parameter. A bifurcation analysis, by means of numerical continuation and the calculation of maximal Lyapunov exponents, reveals interesting phenomena, including bistability and evidence of period-doubling and boundary crisis routes to chaos, that would otherwise not exist in the absence of adaptive coupling. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2407_21393 |
| institution | arXiv |
| publishDate | 2024 |
| record_format | arxiv |
| spellingShingle | Mean-field approximation for networks with synchrony-driven adaptive coupling Fennelly, Niamh Neff, Alannah Lambiotte, Renaud Keane, Andrew Byrne, Áine Neurons and Cognition Synaptic plasticity is a key component of neuronal dynamics, describing the process by which the connections between neurons change in response to experiences. In this study, we extend a network model of $θ$-neuron oscillators to include a realistic form of adaptive plasticity. In place of the less tractable spike-timing-dependent plasticity, we employ recently validated phase-difference-dependent plasticity rules, which adjust coupling strengths based on the relative phases of $θ$-neuron oscillators. We investigate two approaches for implementing this plasticity: pairwise coupling strength updates and global coupling strength updates. A mean-field approximation of the system is derived and we investigate its validity through comparison with the $θ$-neuron simulations across various stability states. The synchrony of the system is examined using the Kuramoto order parameter. A bifurcation analysis, by means of numerical continuation and the calculation of maximal Lyapunov exponents, reveals interesting phenomena, including bistability and evidence of period-doubling and boundary crisis routes to chaos, that would otherwise not exist in the absence of adaptive coupling. |
| title | Mean-field approximation for networks with synchrony-driven adaptive coupling |
| topic | Neurons and Cognition |
| url | https://arxiv.org/abs/2407.21393 |