Neuromorphic computing is an approach to efficiently solve complicated learning and cognition problems like the human brain using electronics. To efficiently implement the functionality of biological neurons, nanodevices and their implementations in circuits are exploited. Here, we describe a general-purpose spiking neuromorphic system that can solve on-the-fly learning problems, based on magnetic domain wall analog memristors (MAMs) that exhibit many different states with persistence over the lifetime of the device. The research includes micromagnetic and SPICE modeling of the MAM, CMOS neuromorphic analog circuit design of synapses incorporating the MAM, and the design of hybrid CMOS/MAM spiking neuronal networks in which the MAM provides variable synapse strength with persistence. Using this neuronal neuromorphic system, simulations show that the MAM-boosted neuromorphic system can achieve persistence, can demonstrate deterministic fast on-the-fly learning with the potential for reduced circuitry complexity, and can provide increased capabilities over an all-CMOS implementation.