Geodesic
The model of interacting social entities
Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 107-118.

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The article produces the generalization of the mathematical model constructed and studied in [1]–[4], to the case of not one, but two interacting social entities. The general problem description is given, provided with definition and notation for corresponding variables. The basic concepts, suggestions and hypotheses are formulated (including, as in [1]–[4], the main concepts of socio-psychological potential, common personality, and the modified hypothesis about imitative behavior). From the mathematical point of view, the model is structured as non-linear dynamic autonomous fourth-order or second-order ODE system, available for numerical and analytical solution. In some partial cases, the closed-form solutions are adduced, providing a rough notion for time-periodical regimes of mutual electorates evolution. 
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V. A. Shvedovskii; P. A. Mikhailova. The model of interacting social entities. Matematičeskoe modelirovanie, Tome 20 (2008) no. 7, pp. 107-118. http://geodesic.mathdoc.fr/item/MM_2008_20_7_a9/

[1] Shvedovskii V. A., “Dinamicheskaya model elektoralnogo povedeniya”, Matem. modelirovanie, 12:8 (2000), 46–56 | MR

[2] Shvedovskii V. A., “Dinamicheskaya model etnopoliticheskogo konflikta: postroenie, vozmozhnosti i rezultaty primeneniya”, Matematicheskoe modelirovanie sotsialnykh protsessov, Vyp. 2, MGU im. M. V. Lomonosova, M., 2000, 31–37

[3] Shvedovskii V. A., Petrova M. A., “Matematicheskoe modelirovanie dinamiki napryazhennosti etnopoliticheskogo konflikta”, Sotsiologiya 4M: metodologiya, metody, matematicheskie modeli, 14 (2002), 151–175

[4] Mikhailov A. P., Shvedovskii V. A., “Rasshirennaya model vybora pozitsii sotsialnoi obschnostyu”, Matematicheskoe modelirovanie sotsialnykh protsessov, Vyp. 5, MGU im. M. V. Lomonosova, MAKS Press, M., 2003, 23–30

[5] Yu.M. Zabrodin i A. P. Pakhomov (red.), Psikhofizika diskretnykh i nepreryvnykh zadach, Nauka, M., 1985

[6] A. N. Lebedev (red.), Psikhofiziologicheskie zakonomernosti vospriyatiya i pamyati, Nauka, M., 1985

[7] Arnold V. I., Kozlov V. V., Neishtadt A. I., Matematicheskie aspekty klassicheskoi i nebesnoi mekhaniki, M., 2002, 416 pp.