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Area of Science:

  • Ecology
  • Mathematical Biology
  • Environmental Science

Background:

  • Ecosystems exhibit self-organized spatial patterns and multistability.
  • Tristability, involving uniform and patterned states, is observed in dryland models.
  • This phenomenon significantly impacts ecosystem behavior under environmental change.

Purpose of the Study:

  • To determine the parameter space extent of tristability in a dryland ecosystem model.
  • To explore the effects of tristability on system dynamics and implications for regime shifts.
  • To analyze the bifurcation structure and interactions of uniform, patterned, and hybrid states.

Main Methods:

  • Utilized a simple mathematical model to simulate ecosystem dynamics.
  • Analyzed bifurcation structures of uniform, periodic, and hybrid states.
  • Mapped parameter space for state existence and interactions.

Main Results:

  • Identified the parameter space for tristability, including uniform, patterned, and hybrid states.
  • Discovered the breakdown of homoclinic snaking structures at a Maxwell point.
  • Revealed a new series of complex fronts with distinct velocities between uniform states.

Conclusions:

  • Tristability significantly influences regime shift dynamics in ecosystems.
  • Findings offer insights into the control of ecosystem state transitions.
  • The study highlights the importance of spatial patterns and multistability in ecosystem resilience.