Studying relationships from the perspective of chaos theory

doi:10.1088/1674-1056/ae27b6

Abstract The study of relationship emotions, a set of emotional and psychological responses that arise in a relationship, can help develop more humanized artificial intelligence, improve human-computer interaction, and even create more immersive experiences in virtual and augmented reality. Due to the nonlinear and feedback-driven nature of relational affect, which aligns closely with chaos theory, and the ability of leaky integrate-and-fire (LIF) neuron models to simulate dopamine-related electrical activity in brain nuclei, this study innovatively integrates both approaches. By linking the membrane potential signals of LIF neurons to relational affect equations, it achieves a refined modeling of the mechanisms underlying relational affect generation. This paper adds the LIF neuron model to the relationship emotion model to construct a new LIF relationship emotion model (LRM). The effect of the parameters in the LRM on the relationship emotions generated by the model is investigated using numerical analysis. This includes the firing behavior produced by LIF neurons and a study of relationship emotions produced by different initial relationship emotion states under the same conditions. Finally, the feasibility of LRM is verified using a digital signal processing (DSP) platform. This process not only verifies the feasibility of LRM but also provides new ideas and methods for future research in affective computing and human-computer interaction.

Keywords: relationship emotion chaos neural network DSP platform

Received: 23 October 2025
Revised: 17 November 2025
Accepted manuscript online: 04 December 2025

PACS:	05.45.Gg	(Control of chaos, applications of chaos)
	05.45.Jn	(High-dimensional chaos)

Fund: This work was supported by the National Natural Science Foundation of China (Grant No. 62571079), the Doctoral Research Startup Fund Program Project of Liaoning Province (Grant No. 2025-BS-0471), the Basic scientific research projects in department of education of Liaoning Province (Grant No. LJ212410152011), and the Research startup fund project for introducing talents of Dalian Polytechnic University (Grant No. LJBKY2025070).

Corresponding Authors: Xianying Xu, Xiaodong Liu
E-mail: xuxiany@dlpu.edu.cn;liuxiaod@dlpu.edu.cn

Cite this article:

Xiyu Ren(任玺谕), Xianying Xu(徐宪莹), Xiaodong Liu(刘晓东), Minghui Zhang(张明会), Santo Banerjee, Suo Gao(高锁), and Jun Mou(牟俊) Studying relationships from the perspective of chaos theory 2026 Chin. Phys. B 35 060504

[1] Zeki S 2007 FEBS Lett. 581 2575
[2] Stanley S M, Rhoades G K and Whitton SW2010 J. Fam. Theory Rev. 2 243
[3] Collins W A 2003 J. Res. Adolesc. 13 1
[4] Acevedo B P, Aron A, Fisher H E and Brown L L 2012 Soc. Cogn. Affect. Neurosci. 7 145
[5] Nieoullon A and Coquerel A 2003 Curr. Opin. Neurol. 16 S3
[6] Chen G, Lai S, Bao G, et al. 2023 Cell Rep. 42 112345
[7] Takahashi K, Mizuno K, Sasaki A T, et al. 2015 Front. Hum. Neurosci. 9 191
[8] Zaki J and Williams W C 2013 Psychol. Bull. 139 803
[9] Ma J 2025 Nonlinear Dyn. 113 25365
[10] Zhao L and Ma J 2025 Chaos 35 023158
[11] Guo Y, Wang C and Ma J 2013 Chaos Solitons Fractals 189 115739
[12] Carl J R, Soskin D P, Kerns C and Barlow D H 2013 Clin. Psychol. Rev. 33 343
[13] Lee J and Pistole M C 2012 J. Couns. Psychol. 59 303
[14] Mou J, Ma T, Banerjee S and Zhang Y 2024 IEEE Trans. Circuits Syst. I Regul. Pap. 71 1771
[15] Njitacke Z T, Isaac S D, Nestor T and Kengne J 2021 Neural Comput. Appl. 33 6733
[16] Shi X, Duan S, Wang L, Huang T and Li C 2015 Neurocomputing 166 487
[17] Xu B, Luo X, Wang Y, Bai L, Chen K and Zhao J 2024 IEEE Trans. Ind. Inf. 20 8673
[18] Xu B, She X, Jiang L, Zou S, Qiu G and Zhao J 2023 Chaos Solitons Fractals 173 113661
[19] Ding S,Wang N, Bao H, Chen B,Wu H and Xu Q 2023 Chaos Solitons Fractals 166 112899
[20] Lin H, Wang C, Sun J, Zhang X, Sun Y and Iu H H C 2023 Chaos Solitons Fractals 166 112905
[21] Rusbult C E and Van Lange P A M 2003 Annu. Rev. Psychol. 54 351
[22] Givertz M and Safford S 2011 Curr. Psychol. 30 148
[23] Mou J, Cao H, Zhou N and Cao Y 2024 IEEE Trans. Cybern. 54 7333
[24] Lin H, Wang C, Xu C, Zhang X and Iu H H C 2022 IEEE Trans. Comput. Aided Des. Integr. Circuits Syst. 42 942
[25] Lin H, Wang C, Sun Y and Wang T 2022 IEEE Trans. Circuits Syst. II Express Briefs 70 311
[26] Di Ventra M, Pershin Y V and Chua L O 2009 Proc. IEEE 97 1717
[27] Li C, Li Y, Yu W, Moroz I and Volos C 2025 Nonlinear Dyn. 113 3857
[28] Xu B, Luo X, Wang Y, Bai L, Chen K and Zhao J 2024 IEEE Trans. Ind. Inf. 20 8673
[29] Wang M, Ding J, Zhang X, Iu H H C and Li Z 2025 Nonlinear Dyn. 113 1879
[30] Wang M, Yi Z and Li Z 2025 Chaos Solitons Fractals 190 115740
[31] Yu Z, Zhu K, Wang Y and Yang F 2025 Chaos Solitons Fractals 194 116233
[32] Yang F, Song X and Yu Z 2025 Nonlinear Dyn. 113 7213
[33] Rinaldi S 1998 SIAM J. Appl. Math. 58 1205
[34] Rinaldi S 1998 Appl. Math. Comput. 95 181
[35] Sprott J C 2004 Nonlinear Dyn. Psychol. Life Sci. 8 303
[36] Liao X and Ran J 2007 Chaos Solitons Fractals 31 853
[37] Gragnani A, Rinaldi S and Feichtinger G 1997 Int. J. Bifurcat. Chaos 7 2611
[38] Sprott J C 2005 Nonlinear Dyn. Psychol. Life Sci. 9 23
[39] Barley K and Cherif A 2011 Appl. Math. Comput. 217 6273
[40] Korn H and Faure P 2003 C. R. Biol. 326 787
[41] Shimada I and Nagashima T 1979 Prog. Theor. Phys. 61 1605
[42] Baron-Cohen S, Knickmeyer R C and BelmonteMK 2005 Science 310 819
[43] Song X and Yang F 2025 J. Theor. Biol. 599 112034
[44] Yang F, Song X and Yu Z 2024 Chaos Solitons Fractals 188 115496
[45] Gao S, Iu H H C, Erkan U, Ç imşek C, Toktaş A, Cao Y, Wu R, Mou J, Li Q and Wang C 2025 IEEE Trans. Circuits Syst. Video Technol. 35 7706
[46] Gao S, Zhang Z, Iu H H C, Ding S, Mou J, Erkan U, Toktas A, Li Q, Wang C and Cao Y 2025 IEEE Internet Things J. 12 18115
[47] Gao S, Zhang Z, Li Q, Ding S, Iu H H C, Cao Y, Xu X, Wang C and Mou J 2025 IEEE Trans. Dependable Secure Comput. 20(3) 1792– 1805

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