Collective dynamics in the presence of finite-width pulses
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arXiv
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| Main Authors: | , , |
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| Format: | Preprint |
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2021
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| _version_ | 1866914838263889920 |
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| author | Afifurrahman Ullner, Ekkehard Politi, Antonio |
| author_facet | Afifurrahman Ullner, Ekkehard Politi, Antonio |
| contents | The idealisation of neuronal pulses as $δ$-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse-width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions, inspired by leaky integrate-and-fire neurons with delay and type-I phase-response curves. By exploring the role of the pulse-widths for different coupling strengths we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e. the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for $δ$-spikes is smoothed out for finite-width pulses. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2102_03438 |
| institution | arXiv |
| publishDate | 2021 |
| record_format | arxiv |
| spellingShingle | Collective dynamics in the presence of finite-width pulses Afifurrahman Ullner, Ekkehard Politi, Antonio Neurons and Cognition Dynamical Systems Adaptation and Self-Organizing Systems The idealisation of neuronal pulses as $δ$-spikes is a convenient approach in neuroscience but can sometimes lead to erroneous conclusions. We investigate the effect of a finite pulse-width on the dynamics of balanced neuronal networks. In particular, we study two populations of identical excitatory and inhibitory neurons in a random network of phase oscillators coupled through exponential pulses with different widths. We consider three coupling functions, inspired by leaky integrate-and-fire neurons with delay and type-I phase-response curves. By exploring the role of the pulse-widths for different coupling strengths we find a robust collective irregular dynamics, which collapses onto a fully synchronous regime if the inhibitory pulses are sufficiently wider than the excitatory ones. The transition to synchrony is accompanied by hysteretic phenomena (i.e. the co-existence of collective irregular and synchronous dynamics). Our numerical results are supported by a detailed scaling and stability analysis of the fully synchronous solution. A conjectured first-order phase transition emerging for $δ$-spikes is smoothed out for finite-width pulses. |
| title | Collective dynamics in the presence of finite-width pulses |
| topic | Neurons and Cognition Dynamical Systems Adaptation and Self-Organizing Systems |
| url | https://arxiv.org/abs/2102.03438 |