The design of a brain-inspired network of coupled FitzHugh – Nagumo (FN) neurons utilizing an adaptive memristor crossbar architecture is introduced in this work. In order to explore the adaptive memristor crossbar impact on the phase synchronization, we firstly exhibit chimera state structures that form in the proposed FN network by employing a fixed memristor crossbar, whose switching behavior is then enhanced with its inherent stochastic nature. Our findings imply that switching dynamics have a major influence on adaptive synchronization and that chimera states are robust by including device-to-device variability in the switching mechanisms of realistic memristors, therefore paving the way for the design and modeling of chimera states.