Journal
FRACTALS-COMPLEX GEOMETRY PATTERNS AND SCALING IN NATURE AND SOCIETY
Volume 30, Issue 10, Pages -Publisher
WORLD SCIENTIFIC PUBL CO PTE LTD
DOI: 10.1142/S0218348X22401946
Keywords
Fractional-Order Neuron Model; Neuronal Network; Multiplex Network; Synchronization; Master Stability Function
Funding
- Natural Science Foundation of Hunan Province [2020JJ5767]
- Natural Science Foundation of China [61901530]
- Slovenian Research Agency [P1-0403, J1-2457]
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This study investigates synchronization in multiplex neuronal networks composed of fractional-order Hindmarsh-Rose neurons and finds that fractional-order models achieve better synchronization compared to integer-order models. By reducing the derivative order of the model, the required coupling strengths for interlayer or intralayer synchronization can be weakened, and the dependence of synchronization on coupling strength decreases.
Fractional-order models describing neuronal dynamics often exhibit better compatibility with diverse neuronal firing patterns that can be observed experimentally. Due to the overarching significance of synchronization in neuronal dynamics, we here study synchronization in multiplex neuronal networks that are composed of fractional-order Hindmarsh-Rose neurons. We compute the average synchronization error numerically for different derivative orders in dependence on the strength of the links within and between network layers. We find that, in general, fractional-order models synchronize better than integer-order models. In particular, we show that the required interlayer and intralayer coupling strengths for interlayer or intralayer synchronization can be weaker if we reduce the derivative order of the model describing the neuronal dynamics. Furthermore, the dependence of the interlayer or intralayer synchronization on the intralayer or interlayer coupling strength vanishes with decreasing derivative order. To support these results analytically, we use the master stability function approach for the considered multiplex fractional-order neuronal networks, by means of which we obtain sufficient conditions for the interlayer and intralayer synchronizations that are in agreement with numerical results.
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