<p>The construction of neural networks using memristors has been widely studied in the field of brain-like computing. However, there is a relative lack of research on the non-bifurcation regulation of chaos in memristive neural networks. In this paper, a 4D memristive Hopfield neural network (HNN) model with non-bifurcation regulation such as amplitude and offset control is constructed using an absolute value voltage-controlled memristor as a tractor, which can generate chaotic attractors with multiple control types. The multistability of the memristive HNN model is investigated by phase diagrams, Lyapunov exponent spectra, and basins of attraction. Numerical simulations show that the amplitude of partial neuron can be regulated by the memristor coupling parameters, and the internal parameters of the memristor can easily control the offset of neurons in the phase space. More interestingly, when symmetry breaking occurs, the neurons can be offset in different directions depending on the choice of initial values. This system provides the first dynamically controllable memristive HNN model. Finally, a hardware circuit is designed to obtain attractors of arbitrary amplitude or position by selecting the appropriate control resistors. The analog hardware implementation verifies the numerical simulation and the theoretical analysis.</p>