Memristor-coupled heterogeneous Hopfield neural network with switchable activation functions and its synchronization control

Heterogeneous activation functions endow neural networks with unique nonlinear characteristics, while asymmetric coupling network architectures can simulate different brain regions to a certain extent. However, these two aspects have not been simultaneously considered in the biomimetic modeling of Hopfield neural network (HNN). For this purpose, this paper proposes and studies a class of memristor-coupled heterogeneous HNN (MCH-HNN) with switchable activation functions for the first time. This coupled network connects two asymmetric sub-HNNs with heterogeneous activation functions through an innovative exponential-type multi-piecewise memristor and achieves this by switching the activation function types in the sub-HNNs. This original model opens an enlightening new perspective for chaotic neural network research. Notably, MCH-HNN can produce an arbitrarily controllable number of multi-structure attractors, and obtain more diversified multi-structure attractors by switching activation function types, a phenomenon that has never been observed in previous studies. By analyzing key parameters such as equilibrium points, coupling strength, initial values, and amplitude modulation factors of MCH-HNN, its complex dynamics are revealed. For example, interesting initial offset and amplitude control effects, as well as rare mirror/central symmetric multi-structure attractors. Furthermore, the physical feasibility of the coupled network is confirmed through analog circuit design. Finally, an effective adaptive integral sliding mode synchronization control scheme is designed to further highlight the application potential of MCH-HNN.