Energy adaptive regulation of a multifunctional neuron circuit

doi:10.1088/1674-1056/ae1451

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.

Keywords: photothermal sensing neuron pseudo-Hamiltonian energy chaotic firing adaptive temperature control bifurcation analysis

Received: 19 August 2025
Revised: 01 October 2025
Accepted manuscript online: 17 October 2025

PACS:	05.45.-a	(Nonlinear dynamics and chaos)
	05.45.Pq	(Numerical simulations of chaotic systems)
	05.45.Gg	(Control of chaos, applications of chaos)

Fund: This work was supported by the Natural Science Foundation of Chongqing (Grant No. CSTB2024NSCQ-MSX0944).

Corresponding Authors: Xi-kui Hu
E-mail: huxk@cqupt.edu.cn

Cite this article:

Xi-kui Hu(胡锡奎), Juan Yang(杨娟), and Ping Zhou(周平) Energy adaptive regulation of a multifunctional neuron circuit 2026 Chin. Phys. B 35 010503

[1] Gundersen V, Storm-Mathisen J and Bergersen L H 2015 Physiol. Rev. 95 695
[2] Harris K D and Mrsic-Flogel T D 2013 Nature 503 51
[3] Walker E Y, Sinz F H, Cobos E, Muhammad T, Froudarakis E, Fahey P G, Ecker A S, Reimer J, Pitkow X and Tolias A S 2019 Nat. Neurosci. 22 2060
[4] Wang Y Q, Hartung J E, Goad A, et al. 2024 Adv. Healthc. Mater. 13 2302330
[5] Gracheva E O, Ingolia N T, Kelly Y M, Cordero-Morales J F, Hollopeter G, Chesler A T, Sáchez E E, Perez J C,Weissman J S and Julius D 2010 Nature 464 1006
[6] Zhang K X, D’Souza S, Upton B A,, et al. 2020 Nature 585 420
[7] Guo, X E, Sun, Z D, Zhu, Y, et al. 2024 Adv. Mater. 36 2406778
[8] Sharma K and Sharma M 2023 Environ. Res. 236 116826
[9] Blasch E, Cruise R, Aved AJ, Majumder UK and Rovito TV 2019 AI Mag. 40 50
[10] Wang Y, Garg R, Cohen-Karni D and Cohen-Karni T 2023 Nat. Rev. Bioeng. 1 193
[11] Richter L M A and Gjorgjieva J 2017 Curr. Opin. Neurobiol. 46 39
[12] Mishra A, Ghosh S, Dana S K, Kapitaniak T and Hens C 2021 Chaos 31 052101
[13] Xie Y, Yao Z, Hu X and Ma J 2022 Chin. Phys. B 30 120510
[14] Zhou P, Zhang X, Hu X and Ren G 2022 Nonlinear Dynam. 110 1879
[15] Hu X, Zhu S, Yang J, Yao Z, Zhou P and Ma J 2024 Commun. Theor. Phys. 76 105004
[16] Apata C O, Tang Y R, Zhou Y F, Jiang L and Pei QM2024 Chin. Phys. B 33 58704
[17] Bloom M, Evans E and Mouritsen O G 1991 Q. Rev. Biophys. 24 293
[18] Guo Q, Zhou P, Zhang X and Zhu Z 2025 Cogn. Neurodynamics 19 75
[19] Chai X, Wang X, Zhang J, Kong D and Sun G 2025 Commun. Theor. Phys. 77 105003
[20] Yang F F, Ma J and Ren G D 2024 J. Theor. Biol. 578 111686
[21] Wan J Y, Wu F Q, Ma J and Wang W 2024 Chin. Phys. B 33 050504
[22] Yang X, Taylor B,Wu A, Chen Y and Chua L O 2022 IEEE T. Circuits- I 69 1845
[23] Yang F F, Ma J and Wu F Q 2024 Chaos Soliton. Fract. 187 115361
[24] Jiang W, Li J, Liu H, Qian X, Ge Y, Wang L and Duan S2022 Chin. Phys. B 31 040702
[25] Shang C, Sun K,Wang H, Yao Z and He S 2023 Nonlinear Dynam. 111 20347
[26] Xu L, Qi G Y and Ma J 2022 Appl. Math. Model. 101 503
[27] Ding Q, Wu Y, Li T, Yu D and Jia Y 2023 Chaos Soliton. Fract. 171 113464
[28] Njitacke Z T, Awrejcewicz J, Ramakrishnan B, Rajagopal K and Kengne J 2022 Nonlinear Dynam. 107 2867
[29] Li Y N, Ma J and Xie Y 2024 Nonlinear Dynam. 112 7459
[30] Xu Y, Liu M, Zhu Z and Ma J 2020 Chin. Phys. B 29 098704
[31] Yeh F, Jara-Oseguera A and Aldrich R W 2023 P. Natl. Acad. Sci. USA 120 e2301528120
[32] Fossi J T, Deli V, Edima H C, Njitacke Z T, Feudjio K F and Atangana J 2022 Eur. Phys. J. B 95 66
[33] Hu X K, Yang J, Song Z and Zhou P 2025 Phys. Scripta 100 075232
[34] Jia J, Zhou P, Zhang X and Ma J 2024 AEU-Int. J. Electron. C. 174 155069
[35] Sarasola C, Torrealdea F J, d’Anjou A, Moujahid A and GrañM 2004 Phys. Rev. E 69 011606
[36] Alonso L M and Marder E 2020 eLife 9 e55470
[37] Wendering P and Nikoloski Z 2023 Biotechnol. Adv. 67 108203
[38] Wu F Q, Guo Y T and Ma J 2023 Sci. China Technol. Sc. 66 3139

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