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}
}