Compactification at Infinity
The behavior at infinity of solutions of ordinary differential equations in the plane was studied by Poincaré by compactification of the Euclidean plane into the unit two-dimensional sphere S2. The same idea of compactification can be applied to RFDEs. In order to illustrate this, we present here a study on equations obtained by compactification of linear delay equations \(\dot x(t) = Ax(t - 1)\) in ℝ2 and in ℝ (compactified to the sphere S2 and the circle S1, respectively).
KeywordsPeriodic Solution Periodic Orbit Hopf Bifurca Imaginary Axis Euclidean Plane
Unable to display preview. Download preview PDF.