Rate-induced tracking for concave or d-concave transitions in a time-dependent environment with application in ecology

Abstract

This paper investigates biological models that represent the transition equation from a system in the past to a system in the future. It is shown that finite-time Lyapunov exponents calculated along a locally pullback attractive solution are efficient indicators (early-warning signals) of the presence of a tipping point. Precise time-dependent transitions with concave or d-concave variation in the state variable giving rise to scenarios of rate-induced tracking are shown. They are classified depending on the internal dynamics of the set of bounded solutions. Based on this classification, some representative features of these models are investigated by means of a careful numerical analysis.

arXiv comment20 pages, 7 figures; typos corrected, language improved, summary of symbols added

References in corpus (12)

• Parameter shifts for nonautonomous systems in low dimension: Bifurcation- and Rate-induced tipping
• Basin bifurcations, oscillatory instability and rate-induced thresholds for AMOC in a global oceanic box model
• Rate-induced tipping from periodic attractors: partial tipping and connecting orbits
• Critical fluctuations and slowing down of chaos
• Rate-induced tipping and saddle-node bifurcation for a class of quadratic differential equations with nonautonomous asymptotic dynamics
• Bifurcation Theory of Attractors and Minimal Sets in D-Concave Nonautonomous Scalar Ordinary Differential Equations
• Weak topologies for Carathéodory differential equations. Continuous dependence, exponential Dichotomy and attractors
• Critical Transitions in D-Concave Nonautonomous Scalar Ordinary Differential Equations Appearing in Population Dynamics
• Topologies of $L_{loc}^p$ type for Carathéodory functions with applications in non-autonomous differential equations
• Generalized Pitchfork Bifurcations in D-Concave Nonautonomous Scalar Ordinary Differential Equations
• Topologies of continuity for Carathéodory delay differential equations with applications in non-autonomous dynamics
• Critical transitions for scalar nonautonomous systems with concave nonlinearities: some rigorous estimates

Cited by in corpus (4)

• Saddle-node bifurcations for concave in measure and d-concave in measure skewproduct flows with applications to population dynamics and circuits
• Critical Transitions for Asymptotically Concave or D-Concave Nonautonomous Differential Equations with Applications in Ecology
• Concave-convex nonautonomous scalar ordinary differential equations: from bifurcation theory to critical transitions
• Nonautonomous scalar concave-convex differential equations: conditions for uniform stability or bistability in a model of optical fluorescence