The discontinuous matching of two planar linear foci can have three nested crossing limit cycles
By Emilio Freire, Enrique Ponce, Francisco Torres. 2014
66 citations recorded by the source corpus.
The existence and stability of limit cycles in discontinuous piecewise linear systems obtained by the aggregation of two linear systems of focus type and having only one equilibrium point is considered. By using an adequate canonical form with five parameters, a thorough study of some Poincar´e maps is performed. Different bifurcations which are responsible for the appearance of crossing limit cycles are detected and parameter regions with none, one, two and three crossing limit cycles are found. In particular, a first analytical proof of the existence, for certain differential systems in the considered family, of at least three homotopic crossing limit cycles surrounding the equilibrium point, is included. This fact has recently been numerically discovered in a particular example by S. -M. Huan and X. -S. Yang.
Subfields: Biochemistry, Geometry and Topology, Public Health, Environmental and Occupational Health
View Paper: https://www.semanticscholar.org/paper/9e5ce0177ecaee17dce04e14f61eef0c11a54dc2
How researchers see this paper
The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.
In Biochemistry
In Geometry and Topology
Citations in the corpus
- Limit cycles in planar piecewise linear differential systems with nonregular separation line (2016, background): “The existence of other examples with three limit cycles, via bifurcation techniques, can be found in [5, 13].”