2015/07/05 by Thai Son Doan, Doan, Thai Son, Kenneth J. Palmer +3
Computer Science · Engineering · Mathematics · #34A30 #34D05 #37H15 #Control Systems in Engineering #Dynamical Systems (math.DS) #FOS: Mathematics #Nonlinear Dynamics and Pattern Formation #Numerical methods for differential equations #math.DS #msc:34A30 #msc:34D05 #msc:37H15
paper · pdf · doi:10.48550/arxiv.1507.01230
openalex publication_date 2015/07/05 · arxiv created 2016/03/18 · arxiv updated 2016/03/21 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
We develop the Bohl spectrum for nonautonomous linear differential equation on a half line, which is a spectral concept that lies between the Lyapunov and the Sacker--Sell spectrum. We prove that the Bohl spectrum is given by the union of finitely many intervals, and we show by means of an explicit example that the Bohl spectrum does not coincide with the Sacker--Sell spectrum in general. We demonstrate for this example that any higher-order nonlinear perturbation is exponentially stable, although this not evident from the Sacker--Sell spectrum. We also analyze in detail situations in which the Bohl spectrum is identical to the Sacker-Sell spectrum.