A Memristive Heterogeneous Hopfield Neural Network with Bidirectional Offset Boosting: Chaotic Dynamics Analysis and Circuit Implementation

Memristive neural networks have gained significant attention due to their rich nonlinear dynamics, yet most existing models employ identical activation functions, which limits their functionality and dynamical complexity. To address this issue, a Memristive Heterogeneous Hopfield Neural Network (MHHNN) is proposed by assigning different activation functions to different neurons. Numerical investigations reveal its rich functionality and complex behaviors, including chaos-period alternations and transient chaos. Notably, under time-varying excitation, the system exhibits a distinctive bidirectional offset boosting phenomenon, where chaotic attractors split and expand symmetrically in the phase space. Hardware realizability is demonstrated through analog circuit and Field-Programmable Gate Array (FPGA) experiments. Furthermore, a chaos-based pseudo-random number generator is developed, and statistical tests demonstrate that the proposed MHHNN produces chaotic sequences with enhanced randomness, highlighting the advantages of memristive coupling and neuronal heterogeneity.