<p>Collective dynamics in neuronal networks arise from complex interactions among neurons and are not restricted to simple pairwise couplings. Recent studies suggest that higher-order interactions, involving groups of neurons acting collectively, play an important role in shaping large-scale brain dynamics. In this work, we investigate the impact of higher-order interactions on the collective behavior of memristive neuronal networks by constructing a nonlocally coupled Hindmarsh-Rose network that incorporates magnetic flux effects. By systematically varying the higher-order coupling strength and the intensity of the magnetic flux effect, we show that higher-order interactions substantially enhance synchronization and reshape the parameter regions in which chimera states emerge. More importantly, the coupling between higher-order interactions and the memristive Hindmarsh-Rose network gives rise to a breathing chimera state and a phase-wave regime. These states are identified quantitatively using the strength of incoherence, discontinuity measure, and local order parameter. In particular, the breathing chimera is characterized by evaluating the strength of incoherence over different time windows. We further show that the intensity of magnetic flux changes the firing pattern of isolated neurons and thereby alters the synchronization pathway and the threshold of coupling strength for synchronization. These results reveal that collective neuronal dynamics are governed not only by coupling strength but also by the structure of interactions, highlighting the crucial role of higher-order interactions in complex neuronal systems.</p>