Rate-induced tipping can trigger plankton blooms

Vanselow, Anna; Halekotte, Lukas; Pal, Pinaki; Wieczorek, Sebastian; Feudel, Ulrike

doi:10.48550/arxiv.2212.01244

Cited by 2 publications

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“…The model exhibits various transient behaviors depending on the rate of temperature increase, . In this instance, the temperature is a slow variable, similar to zooplankton, because it is an environmental factor that fluctuates over time at a specific rate, [16]. In Figure 1.1 (a) the rate is lower than ≈ .…”

Section: Phytoplankton Populationmentioning

confidence: 97%

“…In (b) the rate is higher and we see a sharp spike in the population density of the phytoplankton represented by the red line and a shorter spike for that of the zooplankton, shown by the grey line. This is an indication of a phytoplankton bloom after a rapid environmental change, [16]. Technically as the rate of environment change increases, it bypasses a threshold which can cause a nonlinear change in the dynamics of the system which we call bifurcation.…”

Section: Phytoplankton Populationmentioning

confidence: 97%

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Bifurcations of a discrete-time Phytoplankton-Zooplankton model

Shiri,

2023

Mathematics

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This work mainly investigates the bifurcation problems and topological classifications of a discrete phytoplankton-zooplankton model, whose continuous version was proposed by Truscott and Brindley in 1994. The model is derived by using the semidiscretization technique. Within this study, trivial and semi-trivial fixed points are identified, as well as an interior fixed point that emerges based on specific parametric conditions.Subsequently, an exploration of their topological classifications is undertaken, employing linear stability theory in the vicinity of the trivial, semi-trivial, and interior fixed points.Leveraging the center manifold theorem and bifurcation theory, it is feasible to derive conditions under which the flip and Neimark-Sacker bifurcations are expected to transpire. To validate these findings and draw conclusions, numerical simulations are conducted which produce proof of a Neimark-Sacker bifurcation. Through these comprehensive analyses and simulations, the main aim of this research is to effectively augment the understanding of the dynamics of the model and affirm the validity of our results.

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Section: Phytoplankton Populationmentioning

confidence: 97%

Section: Phytoplankton Populationmentioning

confidence: 97%

Bifurcations of a discrete-time Phytoplankton-Zooplankton model

Shiri,

2023

Mathematics

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“…Such systems may not even have any critical levels of the external input, but they may have critical rates of change of the external input: they suddenly and unexpectedly move to a different state if the external input changes faster than some critical rate. Although critical rates are less understood than critical levels, they are equally relevant and ubiquitous [6,8,9,12,14,25,62,63,74,82,85,86,88,92,96,110,114,121,[126][127][128][129]131]. In particular, critical rates are of special interest in climate science and ecology in the contexts of global warming, increasing climate variability, and ensuing failure to adapt to changing external conditions: the moving stable state is continuously available, but the system is unable to adjust to its changing position when the change happens slowly but too fast.…”

Section: Motivation: Critical Factors and R-tippingmentioning

confidence: 99%

Rate-induced tipping: thresholds, edge states and connecting orbits

2023

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Rate-induced tipping (R-tipping) occurs when time-variation of input parameters of a dynamical system interacts with system timescales to give genuine nonautonomous instabilities. Such instabilities appear as the input varies at some critical rates and cannot, in general, be understood in terms of autonomous bifurcations in the frozen system with a fixed-in-time input. This paper develops an accessible mathematical framework for R-tipping in multidimensional nonautonomous dynamical systems with an autonomous future limit. We focus on R-tipping via loss of tracking of base attractors that are equilibria in the frozen system, due to crossing what we call regular R-tipping thresholds. These thresholds are anchored at infinity by regular R-tipping edge states: compact normally hyperbolic invariant sets of the autonomous future limit system that have one unstable direction, orientable stable manifold, and lie on a basin boundary. We define R-tipping and critical rates for the nonautonomous system in terms of special solutions that limit to a compact invariant set of the autonomous future limit system that is not an attractor. We focus on the case when the limit set is a regular edge state, introduce the concept of edge tails, and rigorously classify R-tipping into reversible, irreversible, and degenerate cases. The central idea is to use the autonomous dynamics of the future limit system to analyse R-tipping in the nonautonomous system. We compactify the original nonautonomous system to include the limiting autonomous dynamics. Considering regular R-tipping edge states that are equilibria allows us to prove two results. First, we give sufficient conditions for the occurrence of R-tipping in terms of easily testable properties of the frozen system and input variation. Second, we give necessary and sufficient conditions for the occurrence of reversible and irreversible R-tipping in terms of computationally verifiable (heteroclinic) connections to regular R-tipping edge states in the autonomous compactified system.

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Rate-induced tipping can trigger plankton blooms

Cited by 2 publications

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Bifurcations of a discrete-time Phytoplankton-Zooplankton model

Bifurcations of a discrete-time Phytoplankton-Zooplankton model

Rate-induced tipping: thresholds, edge states and connecting orbits

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