关键词: photothermal sensing neuron, pseudo-Hamiltonian energy, chaotic firing, adaptive temperature control, bifurcation analysis

Abstract: This study constructs a dual-capacitor neuron circuit (connected via a memristor) integrated with a phototube and a thermistor to simulate the ability of biological neurons to simultaneously perceive light and thermal stimuli. The circuit model converts photothermal signals into electrical signals, and its dynamic behavior is described using dimensionless equations derived from Kirchhoff's laws. Based on Helmholtz's theorem, a pseudo-Hamiltonian energy function is introduced to characterize the system's energy metabolism. Furthermore, an adaptive control function is proposed to elucidate temperature-dependent firing mechanisms, in which temperature dynamics are regulated by pseudo-Hamiltonian energy. Numerical simulations using the fourth-order Runge—Kutta method, combined with bifurcation diagrams, Lyapunov exponent spectra, and phase portraits, reveal that parameters such as capacitance ratio, phototube voltage amplitude/frequency, temperature, and thermistor reference resistance significantly modulate neuronal firing patterns, inducing transitions between periodic and chaotic states. Periodic states typically exhibit higher average pseudo-Hamiltonian energy than chaotic states. Two-parameter analysis demonstrates that phototube voltage amplitude and temperature jointly govern firing modes, with chaotic behavior emerging within specific parameter ranges. Adaptive control studies show that gain/attenuation factors, energy thresholds, ceiling temperatures, and initial temperatures regulate the timing and magnitude of system temperature saturation. During both heating and cooling phases, temperature dynamics are tightly coupled with pseudo-Hamiltonian energy and neuronal firing activity. These findings validate the circuit's ability to simulate photothermal perception and adaptive temperature regulation, contributing to a deeper understanding of neuronal encoding mechanisms and multimodal sensory processing.

Key words: photothermal sensing neuron, pseudo-Hamiltonian energy, chaotic firing, adaptive temperature control, bifurcation analysis