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Lag synchronization in an unidirectional ring of memristive neurons
Vijeesh Vijayan, Hayder Natiq, Shaher Momani, Viet-Thanh Pham, Matjaž Perc, 2025, original scientific article

Abstract: In recent years, the study of neuronal models has provided significant insights into brain dynamics and neurological disorders. Map-based neuronal models, such as the Rulkov map, have gained considerable popularity due to their computational efficiency and ability to replicate complex neuronal dynamics. We thus here study the collective dynamics of an unidirectional ring network composed of three memristive Rulkov maps, with particular emphasis on synchronization patterns and their dependence on coupling types. By employing electrical and memristive/field couplings, we analyze the emergence of complete synchronization, lag synchronization, and phase synchronization under varying coupling strengths. Our f indings highlight how diffusive-based synaptic pathways modulate synchronization and collective behavior in the network. The presented results also offer new perspectives on the role of coupling functions in shaping neuronal synchronization, and they reveal their deeper implications for understanding pathological brain states and for designing neuromorphic systems.
Keywords: simplicial complex, higher-order network, memristive Rulkov, synchronization, cluster synchronization
Published in DKUM: 25.07.2025; Views: 0; Downloads: 2
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Synchronization in simplicial complexes of memristive Rulkov neurons
Mahtab Mehrabbeik, Sajad Jafari, Matjaž Perc, 2023, original scientific article

Abstract: Simplicial complexes are mathematical constructions that describe higher-order interactions within the interconnecting elements of a network. Such higher-order interactions become increasingly significant in neuronal networks since biological backgrounds and previous outcomes back them. In light of this, the current research explores a higher-order network of the memristive Rulkov model. To that end, the master stability functions are used to evaluate the synchronization of a network with pure pairwise hybrid (electrical and chemical) synapses alongside a network with two-node electrical and multi-node chemical connections. The findings provide good insight into the impact of incorporating higher-order interaction in a network. Compared to two-node chemical synapses, higher-order interactions adjust the synchronization patterns to lower multi-node chemical coupling parameter values. Furthermore, the effect of altering higher-order coupling parameter value on the dynamics of neurons in the synchronization state is researched. It is also shown how increasing network size can enhance synchronization by lowering the value of coupling parameters whereby synchronization occurs. Except for complete synchronization, cluster synchronization is detected for higher electrical coupling strength values wherein the neurons are out of the completed synchronization state.
Keywords: simplicial complex, higher-order network, memristive Rulkov, synchronization, cluster synchronization
Published in DKUM: 11.09.2024; Views: 37; Downloads: 9
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