https://doi.org/10.1140/epjs/s11734-025-01671-3
Regular Article
Synchronization in a neuronal network with delayed hybrid synapses
Xi’an Key Laboratory of Human–Machine Integration and Control Technology for Intelligent Rehabilitation, School of Computer Science, Xijing University, No. 1 Xijing Road, 710123, Xi’an, Shaanxi, People’s Republic of China
Received:
24
February
2025
Accepted:
26
April
2025
Published online:
9
May
2025
Synchronization is a fundamental phenomenon in various fields, particularly in neuronal networks, where it underpins critical biological processes. In this paper, we present a novel investigation into synchronization dynamics in a network of memristive Rulkov neuron models with hybrid synapses, incorporating both short-range electrical and long-range chemical interactions. To enhance biological realism, we introduce delays in chemical synaptic transmission, considering both fixed and random delay scenarios. Our work systematically examines the impact of distinct coupling topologies by exploring four cases: (i) both electrical and chemical synapses are globally coupled, (ii) both follow a small-world structure, (iii) electrical synapses are globally coupled while chemical synapses exhibit small-world connectivity, and (iv) the reverse configuration. By quantifying synchronization error, a robust numerical index of synchrony, we reveal that the structure of chemical synapses plays a pivotal role in determining the level of coherence and the ability to achieve synchronization, while the electrical coupling topology significantly influences sensitivity to delays. Notably, our results demonstrate that globally coupled chemical synapses promote stronger synchronization, but the extent of coherence depends on the electrical network structure and delay values. These findings provide new insights into the intricate interplay between synaptic mechanisms, network topology, and delays in shaping neuronal synchronization, offering valuable guidance for designing and analyzing biologically realistic neuronal networks.
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© The Author(s), under exclusive licence to EDP Sciences, Springer-Verlag GmbH Germany, part of Springer Nature 2025
Springer Nature or its licensor (e.g. a society or other partner) holds exclusive rights to this article under a publishing agreement with the author(s) or other rightsholder(s); author self-archiving of the accepted manuscript version of this article is solely governed by the terms of such publishing agreement and applicable law.
