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Some Results Concerning Periodic Solutions of Plane Autonomous Differential Systems
Author(s) -
Sandqvist A.,
Andersen K. M.
Publication year - 1980
Publication title -
zamm ‐ journal of applied mathematics and mechanics / zeitschrift für angewandte mathematik und mechanik
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.449
H-Index - 51
eISSN - 1521-4001
pISSN - 0044-2267
DOI - 10.1002/zamm.19800601110
Subject(s) - plane (geometry) , bifurcation , differential equation , mathematics , autonomous system (mathematics) , mathematical analysis , differential (mechanical device) , order (exchange) , computer science , physics , geometry , nonlinear system , thermodynamics , artificial intelligence , finance , quantum mechanics , economics
In order to obtain results concerning the possible number of closed trajectories to the plane autonomous system ẋ = P(x, y), ẏ = Q(x, y) a related polar differential equation is considered. Some criteria are derived securing this equation to have at most one, respectively at most two 2π‐periodic solutions — thereby giving corresponding results for the number of closed trajectories to the autonomous system. As an illustration the results are applied to investigate a case of bifurcation in a specific example.