Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits

Abstract

Concave in measure and d-concave in measure nonautonomous scalar ordinary differential equations given by coercive and time-compactible maps have similar properties to equations satisfying considerably more restrictive hypotheses. This paper describes the generalized simple or double saddle-node bifurcation diagrams for one-parametric families of equations of these types, from which the dynamical possibilities for each of the equations follow. This new framework allows the analysis of ``almost stochastic" equations, whose coefficients vary in very large chaotic sets. The results also apply to the analysis of the occurrence of critical transitions for a range of models much larger than in previous approaches.

39 pages, 10 figures

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• Concave-convex nonautonomous scalar ordinary differential equations: from bifurcation theory to critical transitions
• Nonsmooth bifurcations in families of one-dimensional piecewise-linear quasiperiodically forced maps
• Nonautonomous scalar concave-convex differential equations: conditions for uniform stability or bistability in a model of optical fluorescence
• Nonautonomous modelling in Energy Balance Models of climate. Limitations of averaging and climate sensitivity