A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems
Copyright policy )A survey on algebraic and explicit non-algebraic limit cycles in planar differential systems
In the qualitative theory of differential equations in the plane one of the most difficult objects to study is the existence of limit cycles. There are many papers dedicated to this subject. Here we will present a survey mainly dedicated to the algebraic and explicit non-algebraic limit cycles of the polynomial differential systems in R and of the discontinuous piecewise differential systems in R formed by two linear differential systems separated by a straight line. For this class of discontinuous piecewise differential systems the study of their algebraic and explicit non-algebraic limit cycles just is starting. Here we provide the first explicit non-algebraic limit cycle for the discontinuous piecewise linear differential systems. Additionally we recall seven open questions related with these types of limit cycles.
- Autonomous University of Barcelona Spain
- Shanghai Jiao Tong University China (People's Republic of)
Averaging method for ordinary differential equations, explicit limit cycle, polynomial differential system, Non-algebraic limit cycle, Piecewise linear differential system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, piecewise linear differential system, Discontinuous ordinary differential equations, Polynomial differential system, Algebraic limit cycle, non-algebraic limit cycle, algebraic limit cycle, Explicit limit cycle
Averaging method for ordinary differential equations, explicit limit cycle, polynomial differential system, Non-algebraic limit cycle, Piecewise linear differential system, Topological structure of integral curves, singular points, limit cycles of ordinary differential equations, Theory of limit cycles of polynomial and analytic vector fields (existence, uniqueness, bounds, Hilbert's 16th problem and ramifications) for ordinary differential equations, piecewise linear differential system, Discontinuous ordinary differential equations, Polynomial differential system, Algebraic limit cycle, non-algebraic limit cycle, algebraic limit cycle, Explicit limit cycle
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