Bendixson’s negative criterion


Let

𝐱˙=𝐟⁒(𝐱)

be a planar system where 𝐟=(𝐗,𝐘)t and 𝐱=(x,y)t. Furthermore 𝐟∈C1⁒(E) where E is a simply connected region of the plane. If βˆ‚β‘π—βˆ‚β‘x+βˆ‚β‘π˜βˆ‚β‘y (the divergence of the vector field f, βˆ‡β‹…πŸ) is always of the same sign but not identically zero then there are no periodic solution in the region E of the planar system.

Title Bendixson’s negative criterion
Canonical name BendixsonsNegativeCriterion
Date of creation 2013-03-22 13:31:01
Last modified on 2013-03-22 13:31:01
Owner Daume (40)
Last modified by Daume (40)
Numerical id 5
Author Daume (40)
Entry type Theorem
Classification msc 34C25