Multilayer structure-induced collective dynamics in uncoupled memristive Rulkov neurons: Impact of field coupling and intralayer connections

• A multilayered structure with one layer as a shared medium for uncoupled memristive Rulkov neurons is explored. • Hybrid and chemical couplings are adopted as intralayer connections, while interlayer connections are established through field coupling. • The pivotal role of the reversal potential in the dynamics of chemical coupling is highlighted. • Collective dynamics in the uncoupled network are influenced by the coherence level of the flux variables in the coupled layer. • Chimera, two-cluster synchronization , and complete synchronization state are found in the uncoupled neurons. In this study, we explore a multilayered structure in which the coupled oscillators of one layer serve as a shared medium for an uncoupled population of neurons. The layers function based on the memristive Rulkov map, and interlayer connections are established through magnetic flux variables, referred to as field coupling. We adopt both hybrid (electrical and chemical) and exclusively chemical couplings for intralayer connectivity. The study highlights the pivotal role of the reversal potential in the dynamics of chemical coupling, while the firing threshold and sigmoid slope play lesser roles. Synchrony analysis reveals distinct synchronization behaviors between the layers. Notably, although the coupled layer can achieve phase synchrony, it fails to induce comparable synchrony in the uncoupled layer. Our findings also highlight the emergence of distinct collective dynamics in the uncoupled network, influenced by the coherence level of the flux variables in the coupled layer. Specifically, incoherent, two-clustered, and globally synchronized oscillations of flux variables in the coupled layer lead to chimera states, two-cluster synchronization, and complete synchronization in the uncoupled neurons, respectively.