Deciphering the complex behavior of piezoelectric neuron systems through bifurcation analysis with the time-domain minimum residual method

In this study, a bifurcation analysis of the piezoelectric neuron system (PNS) is conducted utilizing the time-domain minimum residual method (TMRM). From a biophysical standpoint, integrating piezoelectric devices into a nonlinear neuron circuit enables the conversion of external pressure or sound wave signals into electrical signals. The primary content of this research are as follows: initially, the piezoelectric neuron system is analytically solved by employing the TMRM, yielding high-precision periodic solutions. Subsequently, a detailed bifurcation analysis is performed leveraging these high-precision solutions. The findings demonstrate that the neuronal system experiences a periodic-doubling bifurcation when the amplitude of external stimuli surpasses a specific threshold. With further increases in the stimulus, this periodic-doubling response evolves into a periodic response. Moreover, changes in cell membrane resistance will lead to complex nonlinear behaviors such as stable or unstable period-1 solutions and stable or unstable and critically stable period-3 solutions in the system. These findings offer a theoretical foundation for the advanced design of intelligent functional neuron arrays and sensors.