Deciphering two delay dynamics of ecological system with generalist predator incorporating competitive interference

In this manuscript, an attempt has been made to understand the delay induced (gestation and carry-over effect delay) dynamics of an ecological system with generalist predator exerted fear and its carry-over effect with competitive interference. The designed model exhibits finite time blow up depending on large initial data. The stability of both the delayed and non-delayed systems have been analyzed along with Hopf-bifurcation analysis. It has been observed that carry-over and fear effects act in opposite way in context of stability control for non-delayed system. The two delay (carry-over effect and gestation delay) have significant impact on the dynamics. The former exhibits both stabilizing and destabilizing role while the latter has a destabilizing tendency on the system dynamics. The blow up phenomena for predator species have been shown numerically by verifying the analytical conditions. Our study incorporates a diverse array of figures and diagrams to illustrate and support our findings. Through the exploration of non-linear models, our research unveils several intriguing characteristics. These insights can prove invaluable for biologists seeking a more detailed and pragmatic understanding of generalist predator–prey systems. The visual representations provided in our study contribute to a comprehensive analysis, enhancing the accessibility and applicability of the findings for researchers and practitioners in the field.