An intuitionistic fuzzy approach for prey-predator harvesting system with toxicity and time delay

This study presents an intuitionistic fuzzy prey-predator model with time delay, where several toxic substances from external sources contaminate the prey and predator species. The system consists of one prey and one predator, with the logistic growth of prey species and predation terms proportional to prey density. This system incorporates Holling type-II functional response and introduces a time delay in harvesting prey species over a precise size or age. The primary focus of this work is to investigate the impact of age or size-selective delay on the system's stability within the intuitionistic fuzzy environment. The model employs triangular intuitionistic fuzzy numbers to account for imprecise biological parameters, and it is converted into an intuitionistic fuzzy model using the Hukuhara derivative. The fuzziness of the model is then resolved using Yager's Ranking method. Without delay, the paper delves into the system's dynamics, examining local and global stability and bionomic considerations. Numerical simulations are performed using MATLAB to validate the theoretical findings.