Open AccessPHASE PORTRAIT OF SECOND-ORDER DYNAMIC SYSTEMS
Author(s) -
Kaloyan Yankov
Publication year - 2018
Publication title -
applied researches in technics, technologies and education
Language(s) - English
Resource type - Journals
eISSN - 1314-8796
pISSN - 1314-8788
DOI - 10.15547/artte.2018.03.007
Subject(s) - phase portrait , ordinary differential equation , set (abstract data type) , differential equation , phase (matter) , order (exchange) , portrait , process (computing) , computer science , stability (learning theory) , sequence (biology) , phase plane , algorithm , mathematics , mathematical analysis , physics , chemistry , art , finance , quantum mechanics , nonlinear system , economics , bifurcation , art history , biochemistry , machine learning , programming language , operating system
The phase portrait of the second and higher order differential equations presents ingraphical form the behavior of the solution set without solving the equation. In this way, the stability of a dynamic system and its long-time behavior can be studied. The article explores the capabilities of Mathcad for analysis of systems by the phase plane method. A sequence of actions using Mathcad's operators to build phase portrait and phase trace analysis is proposed. The approach is illustrated by a model of plasma renin activity after treatment of experimental animals with nicardipine. The identified process is a differential equation of the second order. The algorithm is also applicable to systems of higher order.