<p>Synaptic crosstalk originates from heterosynaptic plasticity and diffuse neuromodulation, which is recognized as a crucial mechanism for information integration and dynamic coordination between biological neurons. To clarify its underlying dynamics, this study proposes a bi-neuron discrete memristive Hopfield neural network (BDMHNN), where a pair of discrete hyperbolic tangent memristors (DHTMs) emulate synaptic weights and to establish a crosstalk channel with tunable strength. Multi-parameter bifurcation diagrams, Lyapunov exponent spectra are adopted to demonstrate that the system can traverse a wide range of dynamical behaviors, including periodic, quasi-periodic, chaotic, and hyperchaotic regimes. To validate these dynamics and approximate experimental settings, recurrence quantification analysis (RQA) is applied to noisy one-dimensional time series to recover and verify these patterns from the perspective of scalar measurements. Additionally, Field Programable Gate Array (FPGA) implementation confirms the discrete map at the circuit level. Evaluations of pseudorandomness further demonstrate the feasibility and application potential of the hyperchaotic map, making it a promising platform for both educational demonstrations and engineering applications.</p>