Piecewise Differential Equations for Prey-Predator Interactions: From Dyadic to Triadic

In this study, the applications of the concept of piecewise differential equations, a powerful mathematical tool for addressing different processes occurring at different time intervals, on prey-predator models were discussed. Thanks to this new concept, we aimed to provide a new perspective for prey-predator models in which ecological processes that start with dyadic interactions can also include triadic interactions after a while. More specifically, two prey-predator models were proposed, one dealing with the different scenarios where a second predator was introduced into an environment with a prey and a predator, and the other where an infected prey was introduced into an environment with a prey and a predator. Numerical simulations were carried out in order to have a graphical representation of the different behavior of these two new models under different scenarios. We strongly believe that this study provides a comprehensive overview of piecewise differential equations and contributions to the field of mathematical biology, especially in modeling prey-predator dynamics.