The pattern dynamics of interneuronal networks with inhibitory synaptic coupling

Ying Xu; Xiaodi Li; Ying Xu; Xiaodi Li

doi:10.3934/math.2025498

AIMS Mathematics

2025, Volume 10, Issue 5: 10976-10993. doi: 10.3934/math.2025498

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Research article

The pattern dynamics of interneuronal networks with inhibitory synaptic coupling

Ying Xu ,
Xiaodi Li ^,

School of Mathematics and Statistics, Shandong Normal University, Ji'nan, 250014, China

Received: 27 March 2025 Revised: 26 April 2025 Accepted: 30 April 2025 Published: 13 May 2025
MSC : 62M10, 92C15

Interneurons modulate the excitability of neural networks and maintain neural activity balance via inhibitory or excitatory synaptic connections. Here, we studied the formation of patterns of interneuronal networks with inhibitory synaptic coupling. We found that both electrical synaptic coupling and inhibitory synaptic coupling play a crucial role in the formation of neural network patterns. In addition, delayed inhibitory synapses can also affect the transition of target waves to chaotic states. As the strength of electrical synaptic coupling increases, the firing behavior of neurons gradually becomes highly ordered. When the inhibitory synaptic delay reaches a critical value, we observe a transition in oscillatory patterns from an ordered state to a synchronized state. We further investigated how inhibitory synaptic conductance influences the formation of oscillatory patterns in the network. The study reveals that increasing synaptic conductance disrupts the structure of target waves, inducing chaotic states such as spiral wave fragmentation, while simultaneously elevating neuronal firing rates.
- inhibitory synaptic coupling,
- target waves,
- pattern,
- neural network,
- electrical synaptic coupling
Citation: Ying Xu, Xiaodi Li. The pattern dynamics of interneuronal networks with inhibitory synaptic coupling[J]. AIMS Mathematics, 2025, 10(5): 10976-10993. doi: 10.3934/math.2025498

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Abstract

Interneurons modulate the excitability of neural networks and maintain neural activity balance via inhibitory or excitatory synaptic connections. Here, we studied the formation of patterns of interneuronal networks with inhibitory synaptic coupling. We found that both electrical synaptic coupling and inhibitory synaptic coupling play a crucial role in the formation of neural network patterns. In addition, delayed inhibitory synapses can also affect the transition of target waves to chaotic states. As the strength of electrical synaptic coupling increases, the firing behavior of neurons gradually becomes highly ordered. When the inhibitory synaptic delay reaches a critical value, we observe a transition in oscillatory patterns from an ordered state to a synchronized state. We further investigated how inhibitory synaptic conductance influences the formation of oscillatory patterns in the network. The study reveals that increasing synaptic conductance disrupts the structure of target waves, inducing chaotic states such as spiral wave fragmentation, while simultaneously elevating neuronal firing rates.

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