Open problems in PDE models for knowledge-based animal movement via nonlocal perception and cognitive mapping

Abstract

The inclusion of cognitive processes, such as perception, learning and memory, are inevitable in mechanistic animal movement modelling. Cognition is the unique feature that distinguishes animal movement from mere particle movement in chemistry or physics. Hence, it is essential to incorporate such knowledge-based processes into animal movement models. We summarize popular deterministic mathematical models derived from first principles and their rigorous analyses. Mathematical rules of thumb will be provided to judge the model rationality. We will briefly present available mathematical techniques and introduce useful measures of success to compare and contrast the possible outcomes. Throughout the review, we propose future mathematical challenges and development in the form of open questions. This topic is timely and cutting-edge in applied mathematics with many intriguing directions to be explored.