Multi-dynamics of travelling bands and pattern formation in a predator-prey model with cubic growth

We analyse a predator-prey model with cubic growth in which animal movement are incorporated. We focus on the behaviour of the bands of animals to understand the global dynamic of the system. Travelling waves analyses are used to describe the time evolution of the system and to examine the interplay between the bands. We also highlight the influence of individuals behaviours on the collective behaviour of the bands. More importantly, we show the multi-dynamics that diffusion can cause, and we illustrate the patterns formed in the model as a result of a new phenomenon called transport-driven instability. This study shows how sustainable ecosystems could manipulate their movement characteristics to remain stable and viable.