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TY - JOUR AU - Pippal, Sarita AU - Ranga, Ajay PY - 2025 DA - 2025/12/10 TI - A Nonlinear Dynamical Model of Divorce Due to Extra-Marital Affairs with Long-Distance and Age-Structured Influences JO - Journal of Nonlinear Dynamics and Applications T2 - Journal of Nonlinear Dynamics and Applications JF - Journal of Nonlinear Dynamics and Applications VL - 1 IS - 2 SP - 76 EP - 98 DO - 10.62762/JNDA.2025.544526 UR - https://www.icck.org/article/abs/JNDA.2025.544526 KW - mathematical modeling KW - marital dynamics KW - social contagion KW - nonlinear systems AB - This study introduces an age-structured compartmental model that analyzes transitions among stable marriages, long-distance relationships, extra-marital affairs, and divorce. Key behavioral parameters include $\lambda$ (transition to long-distance), $\delta$ (reunification), $\alpha_1$ and $\alpha_2$ (affair formation), $\beta$ (reconciliation), $\gamma$ (affair-driven divorce), and $\mu$ (non-affair divorce). The unmarried women's pool is structured by age, governed by an engagement function $\theta(a)$ and inflow $\Lambda(a)$. A nonlinear differential equation system captures how behavioral mechanisms collectively drive marital dynamics over time. Numerical simulations show that higher $\beta$ and $\delta$ enhance stability through reconciliation and reunification, while increases in $\lambda$, $\alpha_1$, and $\alpha_2$ raise affair prevalence and divorce. Larger $\gamma$ and $\mu$ further destabilize marriages, increasing the unmarried population. Bifurcation-style plots reveal the nonlinear interplay among parameters and their influence on equilibrium states. The system admits two meaningful equilibria: an age-only state and an interior coexistence state. Stability is determined by a cubic characteristic polynomial; Routh--Hurwitz conditions yield explicit threshold inequalities. Stability persists when dissolution and extramarital transition rates are low, whereas exceeding these thresholds leads to demographic imbalance or oscillations. Overall, the findings underscore the balance between individual behavior and societal intervention. Strengthening social support and reducing separation incentives are suggested strategies to promote marital stability and reduce divorce prevalence. SN - 3069-6313 PB - Institute of Central Computation and Knowledge LA - English ER -
@article{Pippal2025A,
author = {Sarita Pippal and Ajay Ranga},
title = {A Nonlinear Dynamical Model of Divorce Due to Extra-Marital Affairs with Long-Distance and Age-Structured Influences},
journal = {Journal of Nonlinear Dynamics and Applications},
year = {2025},
volume = {1},
number = {2},
pages = {76-98},
doi = {10.62762/JNDA.2025.544526},
url = {https://www.icck.org/article/abs/JNDA.2025.544526},
abstract = {This study introduces an age-structured compartmental model that analyzes transitions among stable marriages, long-distance relationships, extra-marital affairs, and divorce. Key behavioral parameters include \$\lambda\$ (transition to long-distance), \$\delta\$ (reunification), \$\alpha\_1\$ and \$\alpha\_2\$ (affair formation), \$\beta\$ (reconciliation), \$\gamma\$ (affair-driven divorce), and \$\mu\$ (non-affair divorce). The unmarried women's pool is structured by age, governed by an engagement function \$\theta(a)\$ and inflow \$\Lambda(a)\$. A nonlinear differential equation system captures how behavioral mechanisms collectively drive marital dynamics over time. Numerical simulations show that higher \$\beta\$ and \$\delta\$ enhance stability through reconciliation and reunification, while increases in \$\lambda\$, \$\alpha\_1\$, and \$\alpha\_2\$ raise affair prevalence and divorce. Larger \$\gamma\$ and \$\mu\$ further destabilize marriages, increasing the unmarried population. Bifurcation-style plots reveal the nonlinear interplay among parameters and their influence on equilibrium states. The system admits two meaningful equilibria: an age-only state and an interior coexistence state. Stability is determined by a cubic characteristic polynomial; Routh--Hurwitz conditions yield explicit threshold inequalities. Stability persists when dissolution and extramarital transition rates are low, whereas exceeding these thresholds leads to demographic imbalance or oscillations. Overall, the findings underscore the balance between individual behavior and societal intervention. Strengthening social support and reducing separation incentives are suggested strategies to promote marital stability and reduce divorce prevalence.},
keywords = {mathematical modeling, marital dynamics, social contagion, nonlinear systems},
issn = {3069-6313},
publisher = {Institute of Central Computation and Knowledge}
}
Copyright © 2025 by the Author(s). Published by Institute of Central Computation and Knowledge. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (https://creativecommons.org/licenses/by/4.0/), which permits use, sharing, adaptation, distribution and reproduction in any medium or format, as long as you give appropriate credit to the original author(s) and the source, provide a link to the Creative Commons licence, and indicate if changes were made. 
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