Turing instabilities in prey-predator systems with dormancy of predators

Area of Science:

• Mathematical Biology
• Ecology
• Nonlinear Dynamics

Background:

• Prey-predator models are crucial for understanding ecological dynamics.
• Reaction-diffusion systems exhibit complex spatial patterns.
• Turing instabilities can generate patterns from homogeneous states.

Purpose of the Study:

• To investigate Turing instabilities in prey-predator systems with predator dormancy.
• To develop a criterion for classifying stationary and oscillatory Turing instabilities.
• To analyze the role of predator dormancy in pattern formation.

Main Methods:

• Analysis of stationary and oscillatory Turing instabilities.
• Development of a classification criterion for Turing instabilities.
• Numerical simulations of prey-predator reaction-diffusion models.
• Investigation of spatio-temporal pattern formation.

Main Results:

• A simple criterion was proposed to classify Turing instabilities.
• Numerical simulations revealed transient complex patterns.
• These patterns were mixtures of stable Turing patterns and unstable traveling/standing waves.
• Predator dormancy was found to enhance, not generate, spatio-temporal patterns.

Conclusions:

• Predator dormancy acts as an enhancer of spatio-temporal Turing patterns.
• The proposed criterion aids in understanding pattern formation mechanisms.
• While oscillatory Turing instability can occur, stable traveling waves were not observed in simulations.
• The study contributes to the understanding of pattern complexity in ecological models.