Memristive Hopfield neural network dynamics with heterogeneous activation functions and its application

Activation functions play a crucial in emulating biological neurons within artificial neural networks. However, the exploration of neural networks composed of various activation functions and their associated dynamics have not been noticed yet. This paper proposes a novel method by introducing heterogeneous activation functions into a memristive Hopfield neural network for the first time. The special feature of the proposed model lies not only in its ability to mimic the diversity of brain neurons, providing a more realistic and adaptable frame for artificial neural networks but also in its rich dynamic properties suitable for engineering applications. Theoretical and experimental investigations into the dynamics of the memristive Hopfield neural network are conducted, employing phase portraits, bifurcation diagrams, Lyapunov exponent spectra, 0–1 tests, and bi-parameter dynamic maps. Complex dynamical behaviors, including periodic bursting, chaotic bursting, and chaotic state jump are revealed by the numerical simulations. Furthermore, a hardware implementation of the proposed neural network is designed and validated through circuit simulation software, which is consistent with the numerical simulation and confirms the validity of the proposed model. Finally, an encryption scheme based on the chaotic bursting is also proposed and evaluated. Results demonstrate that the chaotic bursting attractor exhibits excellent randomness, making it well-suited for image encryption applications. The novel exploration of heterogeneous activation neuronal networks in this paper may pave the way for further research in the field of more bionic networks with complex dynamical behaviors and their applications.