Dynamics of a plant-herbivore model

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Host-parasite dynamics are fundamental to ecological stability.
• Understanding plant-herbivore interactions is key to managing ecosystems.

Purpose of the Study:

• To develop a simple host-parasite model for plant-herbivore interactions.
• To investigate the impact of herbivory on plant biomass and population dynamics.
• To identify effective control strategies for managing these interactions.

Main Methods:

• Formulated a two-dimensional discrete-time model.
• Used leaf and herbivore biomass as state variables.
• Analyzed the parameter space including host growth rate and herbivore damage.

Main Results:

• Generated bifurcation diagrams to visualize population dynamics.
• Identified bistability, indicating multiple stable states.
• Observed a crisis of a strange attractor, signifying complex dynamics.

Conclusions:

• Two primary control strategies emerged: reducing herbivore populations below a critical threshold.
• Alternatively, increasing the host plant's growth rate can enhance stability.
• These findings offer insights for ecological management and conservation efforts.