Dynamical Analysis and Hardware Implementation of a Novel Fractional-Order Heterogeneous Hopfield Neural Network with Memristive Coupling

To address the limitations of traditional Hopfield neural networks in characterizing complex neuron-to-neuron interactions and heterogeneous activation mechanisms, this paper proposes a fractional-order heterogeneous memristively coupled Hopfield neural network model. First, a fractional-order extension of the ReLU-type memristor is developed, and its locally active behavior within a specific bias interval is verified. Then, a ReLU-type memristor is introduced to model synaptic crosstalk, achieving coupling between neurons, and is incorporated into a three-neuron network featuring ReLU and tanh heterogeneous activation functions, thereby establishing a fractional-order memristive crosstalk-coupled model. The equilibrium points and their local stability are then analyzed. Numerical results show that the fractional-order memory effect substantially modifies the system’s bifurcation structure and dynamical evolution. As the fractional order and coupling parameters vary, the system can exhibit period-1, multiperiodic, and chaotic behavior, as well as coexisting attractors arising from different initial conditions. Based on the two-parameter dynamical maps and one-dimensional profile verification, the modulation effect of the memristive coupling strength on the location and width of periodic windows and chaotic regions is revealed. Furthermore, the local initial-condition plane, differences in bifurcation branches, and Poincaré sections confirm the existence of pronounced multistability and period–chaos coexistence in the proposed system. Finally, an equivalent circuit is constructed in Multisim, and experimental validation is carried out on the NI-LabVIEW hardware platform, showing good agreement with the numerical findings. The proposed model provides a useful reference for complex dynamical analysis and circuit implementation of fractional-order memristive neural networks.