Bautin bifurcations in a forest-grassland ecosystem with human-environment interactions

Area of Science:

• Ecology
• Mathematical Biology
• Dynamical Systems Theory

Background:

• Ecosystems exhibit complex dynamics, susceptible to sudden, irreversible changes termed catastrophic shifts.
• Mathematical models using differential equations approximate these phenomena, with shifts linked to bifurcation points.

Purpose of the Study:

• To demonstrate how gradual environmental changes can lead to sudden ecosystem shifts via codimension-2 bifurcations.
• To highlight the utility of numerical bifurcation theory for analyzing ecological model criticalities in 2D parameter spaces.

Main Methods:

• Utilized numerical bifurcation theory to analyze a forest-grassland mosaic ecosystem model.
• Constructed a 2D bifurcation diagram considering human influence and natural causes.
• Investigated Bautin bifurcations to characterize transitions.

Main Results:

• Codimension-2 bifurcations can transform smooth ecological changes into abrupt, catastrophic shifts.
• The analyzed forest-grassland model exhibited both abrupt and smooth transitions.
• Bautin bifurcations were identified as a mechanism for these transitions.

Conclusions:

• Gradual changes in ecological systems can precipitate sudden shifts, particularly through codimension-2 bifurcations.
• Numerical bifurcation analysis is crucial for understanding ecosystem stability and predicting critical transitions.
• The forest-grassland model illustrates the complex dynamics that can emerge from simple ecological interactions.