Synchronization in a memristive duplex network: The impact of intra-layer and inter-layer synaptic pathways

•This study investigates how synaptic and field interactions affect synchronization.•Master stability function and synchronization error methods assess stability.•Electrical and inner linking connections facilitate synchronization in networks.•Chemical synapses hinder synchronization, making it harder for neurons to synchronize.•Field coupling enhances inter-layer synchronization when combined with chemical synapses. Synchronization in multiplex networks is crucial for modeling functional connectivity in computational neuroscience. This study analyzes synchronization in a memristive Hindmarsh-Rose duplex network, investigating how synaptic pathways affect synchronization. Initially, electrical, inner-linking, and chemical functions are separately applied to both intra- and inter-layer connections. Then, a more realistic approach combines intra-layer electrical and inner-linking functions with inter-layer chemical synapses. Field coupling is also examined as an inter-layer connection with different intra-layer synapses. Synchronization stability is evaluated using the master stability function and synchronization error. Results show that electrical and inner-linking functions support intra- and inter-layer synchronization as coupling strength increases. However, with chemical synapses, neurons achieve synchronization under limited conditions. Applying chemical synapses to inter-layer connections restricts inter-layer synchronization, although intra-layer synchronization remains observable with electrical or inner-linking functions. Field coupling effectively promotes inter-layer synchronization when paired with intra-layer chemical connections but reduces it with intra-layer electrical or inner-linking functions.