Bio-inspired control systems attract significant interest in the scientific community. The advantage of neural systems lies in their ability to adapt to control processes. Path-following tasks in automated vehicles and advanced driver assistance systems are an essential component related to vehicle safety and performance. It is known that model-based controllers, which integrate a vehicle model into the control logic, are more effective than geometry-based controllers. However, a disadvantage of model-based controllers is the lack of adaptation capability to changing vehicle dynamic conditions. To address this issue, an adaptive neural controller for path-following tasks is proposed based on neural networks, particularly Spiking Neural Networks and Associative Maps. Consequently, associative maps and neural interpolation via the modelling of non-linear synaptic connections are brought to a spiking neural network to perform adaptive control tasks. Neural associative maps are used to derive functional relationships between neural inputs and outputs, further enhancing inference capabilities. In addition, neural interpolation with non-linear synaptic connections enables efficient pairwise association. Thus, by reproducing a linear quadratic regulator with a learning-capable neural network, it is possible to adjust for discrepancies and changes in dynamics through spike-timing-dependent plasticity. Results demonstrate that the adaptive controller is effective in maintaining the initial tracking performance of the vehicle while adapting to changing dynamic conditions with a computational cost that allows real-time execution. The proposed strategy results in lower error levels in lateral tracking after the learning process, while providing similar performance on heading.