The hyperbolic tangent function is a commonly used activation function in Hopfield neurons, where its activation gradient serves as a gain scaling parameter reflecting the response speed of neuronal electrical activity. This paper proposes a novel method of integrating memristors with discretely coupled neural networks by using an exponential memristor as the activation gradient of Neuron 2, and analyzes the impact of its gain on the hyperbolic tangent activation function. Furthermore, a discrete magnetically controlled memristor model combined with sine and square functions is used as subsynapses of Neuron 1, resulting in a Discrete Hopfield neural network (DHNN) model with infinitely many equilibrium points. The results indicate that this DHNN can exhibit complex and diverse dynamical behaviors related to multiple system parameters, including rare hyperchaotic behavior characterized by four positive Lyapunov exponents, discharge mode transitions, and coexistence phenomena. Based on this, an efficient and secure color image encryption scheme is designed, and extensive security analysis shows that the proposed scheme has strong security performance.