Cognitive equilibrium and instability : Lyapunov stability analysis in mental health research

Verma, Vivek Kumar; Saini, Bhavna; Jain, Tarun; Dadheech, Pankaj

doi:10.47974/JIM-1821

Open Access Research Article

Cognitive equilibrium and instability : Lyapunov stability analysis in mental health research

Vivek Kumar Vermavivekkumar.verma@jaipur.manipal.eduDepartment of Information Technology Manipal University JaipurJaipur, Rajasthan, 303007, IndiaView full profile → , Bhavna Sainibhavnasaini10@gmail.comDepartment of Data Science & Analytics Central University RajasthanDepartment of Data Science & Analytics Central University of Rajasthan Rajasthan, IndiaView full profile → , ^*Tarun JainCorresponding authortarunjainjain02@gmail.com; tarun.jain@jaipur.manipal.eduDepartment of Computer Science & Engineering Manipal University JaipurDepartment of Computer Science and Engineering Manipal University Jaipur Jaipur, Rajasthan, 303007, IndiaView full profile → , Pankaj Dadheechpankajdadheech777@gmail.comDepartment of Computer Science & Engineering Swami Keshvanand Institute of Technology, Management & GramothanJaipur, Rajasthan, 302017, IndiaView full profile →

* Corresponding author · click or hover a name for details

pp. 273–283Vol. 27Issue 2March 2024DOI: 10.47974/JIM-1821XML

Published Online:: 19 Mar 2024
Article type:: Research Article
Language:: EN
Article no.:: JIM-1821
Pages:: 273–283

Abstract

Mental well-being is often seen as a fragile state, akin to a tightrope walk of balance. In our paper, “Cognitive Equilibrium and Instability: Lyapunov Stability Analysis in Mental Health Research,” we explore the nuanced dance between consistency and change in the realm of cognitive function. Drawing on Lyapunov Stability principles from the study of dynamic systems, we offer new perspectives on mental health mechanics. We propose that the mind is in a state of perpetual flux, constantly adjusting to a spectrum of influences to maintain cognitive balance. Our work involves identifying these points of balance and assessing their robustness using Lyapunov Stability Analysis. We examine how various factors, such as stress, environmental changes, and biological variations, can disrupt this balance, possibly leading to states of well-being or illness. Through our models, we illuminate the evolution and path of mental health conditions. Our methodology is a synthesis of theoretical models and real-world data, including neuroimaging, clinical, and psychological evaluations. Case studies in our paper demonstrate the application of our models to conditions like anxiety, depression, and bipolar disorder, revealing the fluid nature of these ailments. This work goes on to discuss the practical implications of our findings in the clinical setting. By identifying pivotal points of potential instability, our model serves as a tool for early identification of mental health concerns, guiding the creation of specific therapeutic interventions. Additionally, our work supports a tailored approach to mental health care, appreciating the individual cognitive patterns unique to each person. Our paper contributes to the burgeoning field of computational psychiatry, blending mathematical analysis with a perspective centered on the human experience. It sets the stage for future interdisciplinary research aimed at decoding the intricacies of the human psyche.

Keywords

Lyapunov stability Cognitive equilibrium Dynamic systems theory Mental health dynamics Computational psychiatry Cognitive instability

Subject Classifications

03C45

References

[1] X. Li, D. Peng, and J. Cao, ‘Lyapunov Stability for Impulsive Systems via Event-Triggered Impulsive Control,’ IEEE Transactions on Automatic Control, pp. 4908-4913 (2020).
[2] C. Xu, et al., ‘Lyapunov Stability and Wave Analysis of Covid-19 Omicron Variant of Real Data with Fractional Operator,’ Alexandria Engineering Journal, pp. 11787-11802 (2022).
[3] Sabah, M., Entesar, A., & Qasim, O. S., Hybrid method between Lyapunov’s artificial small parameter and bat algorithm for fractional differential equations. Journal of Interdisciplinary Mathematics, 25(6), 1733-1752 (2022).
[4] R. C. B. Rego and F. M. U. de Araújo, ‘Learning-Based Robust Neuro-Control: A Method to Compute Control Lyapunov Functions,’ International Journal of Robust and Nonlinear Control, pp. 2644-2661 (2022).
[5] P. L. Neves, M. Rodrigues, F. Gonçalves, “The role of EHR patient portals in patient engagement,” Healthcare Informatics Research, pp. 204-210 (2020).
[6] M. Iasiello and J. Van Agteren, ‘Mental Health and/or Mental Illness: A Scoping Review of the Evidence and Implications of the Dual-Continua Model of Mental Health,’ Evidence Base: A Journal of Evidence Reviews in Key Policy Areas, pp. 1-45 (2020).
[7] Q. J. M. Huys, et al., ‘Advances in the Computational Understanding of Mental Illness,’ Neuropsychopharmacology, pp. 3-19 (2021).
[8] Yadav, A., Saini, B., Verma, V. K., & Pal, V., A joint medical image compression and encryption using AMBTC and hybrid chaotic system. Journal of Discrete Mathematical Sciences and Cryptography, 24(8), 2233-2244 (2021).
[9] S. Annas, et al., ‘Stability Analysis and Numerical Simulation of SEIR Model for Pandemic COVID-19 Spread in Indonesia,’ Chaos, Solitons & Fractals, vol. 139, 110072 (2020).
[10] Q. J. M. Huys, et al., ‘Advances in the Computational Understanding of Mental Illness,’ Neuropsychopharmacology, vol. 46, no. 1, pp. 3-19 (2021).
[11] Anticevic, Alan, and John D. Murray, eds. Computational psychiatry: Mathematical modeling of mental illness. Academic Press (2017).
[12] Kumar, Anil , Gupta, Amit Kumar, Panwar, Deepak , Chaurasia, Sandeep & Goyal, Dinesh. Operating system security with discrete mathematical structure for secure round robin scheduling method with intelligent time quantum, Journal of Discrete Mathematical Sciences and Cryptography, 26:5, 1519–1533 (2023).
[13] Kushwaha, Satpal Singh, Joshi, Sandeep & Gupta, Amit Kumar. An efficient approach to secure smart contract of Ethereum blockchain using hybrid security analysis approach, Journal of Discrete Mathematical Sciences and Cryptography, 26:5, 1499–1517 (2023), DOI: https://doi.org/10.47974/JDMSC-1815.
[14] Joshi, Ruchi, Mathur, Priya, Gupta, Amit Kumar, Singh, Suyesha, Paliwal, Vismita & Nayar, Sejal. Mathematical modeling of intelligent system for predicting effectiveness of premenstrual syndrome, Journal of Interdisciplinary Mathematics, 26:3, 551-562 (2023).

Views: 232Downloads: 9Citations: 0