Critical Transitions in Piecewise Uniformly Continuous Concave Quadratic Ordinary Differential Equations

Abstract A critical transition for a system modelled by concave quadratic scalar ordinary differential equation occurs when small variation of the coefficients changes dramatically dynamics, from existence an attractor–repeller pair hyperbolic solutions to lack bounded solutions. In this paper, tool analyze phenomenon asymptotically nonautonomous ODEs with uniformly continuous or piecewise is described, and used determine occurrence transitions certain parametric equations. Some numerical experiments contribute clarify applicability tool.