Building neural network models and studying their dynamic behaviours is extremely important from both a theoretical and practical standpoint due to the rapid advancement of artificial intelligence. In addition to its engineering applications, this article concentrates primarily on the memristor model and chaotic dynamics of the asymmetric memristive neural network. First, we develop a novel-multistable, highly-tunable memristor model. Using this memristor model to build an asymmetric memristive neural network (AMNN), the chaotic dynamics of the proposed AMNN are investigated and analyzed using fundamental dynamics techniques such as equilibrium stability, bifurcation diagrams, and Lyapunov exponents. According to the findings of this study, the proposed AMNN possesses a number of complex dynamic properties, including scaling amplitude hyperchaos with coupling strength control, and coexisting unusual chaotic attractors with ini-