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## Investigation of the Dynamic Systems’ Phase Portraits

#### İrina ANDREEVA [1] , Tatiana EFIMOVA [2]

Dynamic systems in a broad sense may be considered as mathematical models of processes and phenomena, where any statistical events we may disregard. The dynamic systems theory investigates curves, defined by differential equations. The same time the laws of Nature are written using the language of differential equations, as the great French mathematician and encyclopedist of the nineteenth and twentieth centuries J.H. Poincare has taught. Thus, these laws are written using dynamic systems. A study of a given family of dynamic systems depending on several parameters means splitting of a phase space belonging to the dynamic system under consideration into trajectories and investigation of the limit behavior of them with the aim to reveal and describe their positions of equilibrium, and to find the so-called sinks and sources. Also, very important are the question of the stability of equilibrium states and their types, as well as the question of a roughness of a system. Rough dynamic systems can preserve their qualitative character of motion under some considerably small changes in parameters of the system. The paper is devoted to the original investigation of a broad family of polynomial dynamic systems, depending on multiple parameters.
Dynamic systems, Trajectories, Phase portraits, Equilibrium states, Differential equations, Poincare sphere, Poincare disk, Singular points, Separatrices, Limit cycles
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Birincil Dil en Mühendislik Makaleler Yazar: İrina ANDREEVA Kurum: Peter the Great St. Petersburg Polytechnic UniversityÜlke: Romania Yazar: Tatiana EFIMOVA Kurum: Peter the Great St. Petersburg Polytechnic UniversityÜlke: Russian Federation Yayımlanma Tarihi : 24 Kasım 2019
 Bibtex @araştırma makalesi { epstem656429, journal = {The Eurasia Proceedings of Science Technology Engineering and Mathematics}, issn = {}, eissn = {2602-3199}, address = {isresoffice@gmail.com}, publisher = {ISRES Organizasyon Turizm Eğitim Danışmanlık Ltd. Şti.}, year = {2019}, volume = {7}, pages = {338 - 345}, doi = {}, title = {Investigation of the Dynamic Systems’ Phase Portraits}, key = {cite}, author = {ANDREEVA, İrina and EFIMOVA, Tatiana} } APA ANDREEVA, İ , EFIMOVA, T . (2019). Investigation of the Dynamic Systems’ Phase Portraits. The Eurasia Proceedings of Science Technology Engineering and Mathematics , 7 () , 338-345 . Retrieved from https://dergipark.org.tr/tr/pub/epstem/issue/50288/656429 MLA ANDREEVA, İ , EFIMOVA, T . "Investigation of the Dynamic Systems’ Phase Portraits". The Eurasia Proceedings of Science Technology Engineering and Mathematics 7 (2019 ): 338-345 Chicago ANDREEVA, İ , EFIMOVA, T . "Investigation of the Dynamic Systems’ Phase Portraits". The Eurasia Proceedings of Science Technology Engineering and Mathematics 7 (2019 ): 338-345 RIS TY - JOUR T1 - Investigation of the Dynamic Systems’ Phase Portraits AU - İrina ANDREEVA , Tatiana EFIMOVA Y1 - 2019 PY - 2019 N1 - DO - T2 - The Eurasia Proceedings of Science Technology Engineering and Mathematics JF - Journal JO - JOR SP - 338 EP - 345 VL - 7 IS - SN - -2602-3199 M3 - UR - Y2 - 2020 ER - EndNote %0 The Eurasia Proceedings of Science Technology Engineering and Mathematics Investigation of the Dynamic Systems’ Phase Portraits %A İrina ANDREEVA , Tatiana EFIMOVA %T Investigation of the Dynamic Systems’ Phase Portraits %D 2019 %J The Eurasia Proceedings of Science Technology Engineering and Mathematics %P -2602-3199 %V 7 %N %R %U ISNAD ANDREEVA, İrina , EFIMOVA, Tatiana . "Investigation of the Dynamic Systems’ Phase Portraits". The Eurasia Proceedings of Science Technology Engineering and Mathematics 7 / (Kasım 2019): 338-345 . AMA ANDREEVA İ , EFIMOVA T . Investigation of the Dynamic Systems’ Phase Portraits. EPSTEM. 2019; 7: 338-345. Vancouver ANDREEVA İ , EFIMOVA T . Investigation of the Dynamic Systems’ Phase Portraits. The Eurasia Proceedings of Science Technology Engineering and Mathematics. 2019; 7: 345-338.

Makalenin Yazarları
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