<p>The adoption of diverse memristors to simulate autapses achieves bionic simulation, providing new idea for the dynamical research of artificial neural networks. To realize this idea, this paper explores the local activity and nonvolatility of the locally-active memristor, and then constructs a memristive Hopfield neural network (MHNN) with employing three memristors to simulate heterogeneous autapses. Importantly, a unique memristor-driven offset-boosting is discovered by adjusting the parameter of each memristor. The directional regulation of attractor can be achieved in the direction of the corresponding state variable. By regulating the initial conditions, the rich multistable behaviors are revealed through coexisting bifurcation diagrams and attraction basin. Based on the synaptic plasticity mechanism, the autaptic weights of MHNN are changed to observe the different states of attractors. Subsequently, attractors are captured using Field Programmable Gate Array (FPGA), which proves the feasibility of MHNN. Finally, by designing the synchronous controllers, the synchronous control between the two neural networks is achieved, making MHNN have a good engineering application prospect.</p>