Presentation Information
[SS18-03]Stochastic Differential Equations for Ecological Modeling: Applications to Swarms and Predator-Prey
*Ton Viet Ta1 (1. Laboratory of Mathematical Modeling, Kyushu University (Japan))
Keywords:
Stochastic Differential Equations,Swarms,Predator-Prey
This presentation investigates the role of noise in ecological systems, examining both swarm behavior and predator-prey interactions. We develop models for these phenomena using stochastic differential equations, establishing the existence and uniqueness of solutions. We then demonstrate that when noise is low, the local rules underlying swarm formation are structurally stable, and predator-prey systems exhibit sustainable dynamics. However, exceeding a critical noise threshold disrupts this structural stability. Numerical simulations are provided to support and visualize these analytical results.