Critical transitions in piecewise uniformly continuous concave quadratic ordinary differential equations

Abstract

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

41 pages, 7 figures

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• Basin bifurcations, oscillatory instability and rate-induced thresholds for AMOC in a global oceanic box model
• Phase tipping: How cyclic ecosystems respond to contemporary climate
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Cited by in corpus (1)

• Critical Transitions in D-Concave Nonautonomous Scalar Ordinary Differential Equations Appearing in Population Dynamics