Rectifiability of orbits for two-dimensional nonautonomous differential systems

Abstract

The present study is concerned with the rectifiability of orbits for the two-dimensional nonautonomous differential systems. Criteria are given whether the orbit has a finite length (rectifiable) or not (nonrectifiable). The global attractivity of the zero solution is also discussed. In the linear case, a necessary and sufficient condition can be obtained. Some examples and numerical simulations are presented to explain the results.

Keywords

• rectifiability
• global attractivity
• two-dimensional nonautonomous system