Asymptotic Dissipativity of Lorenz model with Markov Switching for the City Development

Автор(и)

  • Анастасія Володимирівна Кінаш Національний університет "Львівська політехніка", Україна
  • Уляна Теодорівна Хімка Національний університет "Львівська політехніка", Україна

DOI:

https://doi.org/10.32626/2308-5878.2016-13.78-86

Ключові слова:

Lorenz model, city system, asymptotic dissipativity, stationary point

Анотація

In the work activity of the city system, described by generalized Lorentz model, is considered. It is assumed the existence of external influence on the land rate change in the city that is described by diffusive term and ergodic Markov processes. With the made assumptions, asymptotic dissipativity conditions of the initial system are set. Stationary points of the model of city economical activity are studied based on the results obtained for asymptotic dissipativity of generalized Lorentz model.

Посилання

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Kinash A. V. Asymptotic dissipativity of the diffusion process. процесу / A. V. Kinash, Ya. M. Chabanyuk, U. T. Khimka // Mathematical and computer modeling. A series of physical and mathematical sciences. Collected Works. V.M. Glushkov Institute of Cybernetics, Kamyanets-Podilsky national univer-sity of I. Ogiienko. — 2014. — Issue. 11. — P. 77–87. (in Ukrainian).

Beliavskii S. S. The generalized model of urban system (generalized Lorenz system) / S. S. Beliavskii, T. A. Orlianin // Third International Scientific Con-ference «Mathematical Modeling and Differential Equations»: a collection of articles of the Third International Scientific Conference. Brest, September 17–22, 2012. — Minsk : BGU, 2012. — P. 70-78. (in Russian).

Bondarev B. V. Stochastic calculus in problems of financial and actuarial mathematics. Risk assessment for insurance / B. V. Bondarev, О. Е. Sosnitz-kii. — 2013. — 228 p. (in Russian).

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Опубліковано

2016-03-17

Номер

2016: Математичне та комп'ютерне моделювання. Серія: Фізико-математичні науки. Випуск 13

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Статті

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