Periodic solutions of Abel differential equations
Copyright policy )Periodic solutions of Abel differential equations
For a class of polynomial non-autonomous differential equations of degree n, we use phase plane analysis to show that each equation in this class has n periodic solutions. The result implies that certain rigid two-dimensional systems have at most one limit cycle which appears through multiple Hopf bifurcation.
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Abel differential equation, Applied Mathematics, periodic solution, Limit cycle, Dynamical Systems (math.DS), abel differential equation, limit cycle, Rigid system, Periodic solution, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hopf bifurcation, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Mathematics - Dynamical Systems, Periodic solutions to ordinary differential equations, 34C, Analysis, rigid system
Abel differential equation, Applied Mathematics, periodic solution, Limit cycle, Dynamical Systems (math.DS), abel differential equation, limit cycle, Rigid system, Periodic solution, Mathematics - Classical Analysis and ODEs, Classical Analysis and ODEs (math.CA), FOS: Mathematics, Hopf bifurcation, Entire and meromorphic solutions to ordinary differential equations in the complex domain, Mathematics - Dynamical Systems, Periodic solutions to ordinary differential equations, 34C, Analysis, rigid system
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