Robust security is essential to protect sensitive medical images against evolving cyber threats, such as unauthorized access and data breaches, where traditional encryption methods often fail due to limitations of encoding keys and computation time. This research employs the complex chaotic dynamics exhibited by an electromagnetic radiation-stimulated Hopfield neural network (HNN) to develop a novel compressive sensing-based encryption framework. Detailed analysis of the HNN model, facilitated by two-parameter charts, uncovered its inherent capacity for diverse dynamical behaviors, including chaotic oscillations and periodic states. Significantly, a distinctive butterfly-like chaotic attractor was identified within the system’s phase portrait, visually demonstrating its profound inherent complexity. Using these intricate chaotic dynamics, we specifically engineered a dedicated and robust compressive sensing cryptosystem to secure medical images. The resulting encryption scheme delivers demonstrably high security, evidenced by rigorous statistical performance metrics, including entropy and correlation coefficients, alongside significant resilience against adversarial clipping attacks. This work presents a promising cryptographic approach that effectively utilizes the engineered and unpredictable properties of the stimulated HNN to enhance both the confidentiality and integrity of digital medical imaging data during storage and transmission.