A Continuous Model of Marital Relations with Stochastic Differential Equations
Abstract
:1. Introduction
1.1. Continuous Model
Deterministic Case
1.2. Stochastic Model
2. Analysis of the Deterministic Case
Qualitative Analysis for the Bilinear Influence Function
- (1)
- A saddle point if:
- (2)
- A node if:It will be stable if or unstable if .
- (3)
- A spiral if:
- (4)
- A center if:
- (5)
- A proper or improper node if:
- (i)
- Saddle points (and therefore unstable) if and only if , and or
- (ii)
- Stable nodes if and only if and .
3. Numerical Simulations
3.1. Single Individual with Validating Personality
3.2. Validating Wife and Husband with Bilinear Influence Function
3.3. Piece-Wise Influence Function
3.4. Piece-Wise Linear Influence Function
4. Conclusions
Author Contributions
Funding
Acknowledgments
Conflicts of Interest
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Figure Number | Type of Influence Function | Parameters |
---|---|---|
2 | Zero influence function | , . |
3 | Bilinear | , , , , ; , , . |
4 | Piece-wise constant | , , , , , , |
5 | Piece-wise constant | , , , , , , , |
6 | Piece-wise constant with saturation | , , , , , , , |
7 and 8 | Piece-wise linear | , , ; , , |
9 and 10 | Piece-wise cubic | , , ; , , |
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Chen-Charpentier, B.; Garza-Hume, C.E.; Jorge, M.d.C. A Continuous Model of Marital Relations with Stochastic Differential Equations. Math. Comput. Appl. 2021, 26, 3. https://doi.org/10.3390/mca26010003
Chen-Charpentier B, Garza-Hume CE, Jorge MdC. A Continuous Model of Marital Relations with Stochastic Differential Equations. Mathematical and Computational Applications. 2021; 26(1):3. https://doi.org/10.3390/mca26010003
Chicago/Turabian StyleChen-Charpentier, Benito, Clara Eugenia Garza-Hume, and María del Carmen Jorge. 2021. "A Continuous Model of Marital Relations with Stochastic Differential Equations" Mathematical and Computational Applications 26, no. 1: 3. https://doi.org/10.3390/mca26010003