Lag synchronization in an unidirectional ring of memristive neurons

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 findings 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.