Predator-prey model with fuzzy parameters and fuzzy initial conditions: a systematic literature review

Abstract

A predator-prey model with fuzzy parameters and fuzzy initial conditions is a model of interaction between species that takes into account uncertainty in both parameters and initial conditions expressed in fuzzy numbers. Over the past years, numerous studies have been conducted on this model. This paper provides a review of research carried out by several previous scholars in developing and studying this model, focusing on the model evolution and the methodologies employed. The review reveals that starting in 2015, researchers began expanding the fuzzy predator-prey models by incorporating additional biological processes, such as considering harvesting factors, disease, prey protection, toxic effects, etc. Various approaches, including the Hukuhara derivative (H-derivative) approach, the generalized Hukuhara derivative (gH-derivative) approach, and the Zadeh extension principle approach, were utilized to study the predator-prey fuzzy model. Based on the findings of this review, there are still opportunities for further predator-prey fuzzy model development by incorporating additional biological factors, such as Allee effects. Furthermore, the limitations associated with the employed methodologies indicate potential for future research exploring alternative approaches to fuzzy derivatives, such as generalized derivative (g-derivatives) and granular derivatives (gr-derivatives). Another development that can be carried out for further research is to combine parameters and initial conditions as a fuzzy uncertainty so that it is more realistic and in accordance with real conditions.