# Dynamics and Control of Additional Food Provided Prey-Predator Systems exhibiting Holling Type-III Functional Response and Intra-specific Competition among Predators Source: [Dynamics and Control of Additional Food Provided Prey-Predator Systems exhibiting Holling Type-III Functional Response and Intra-specific Competition among Predators]() Collection index: [llms.txt]() Data updated: 2025-10-25T18:10:08.153Z Authors: D Bhanu Prakash, D K K Vamsi Published: 2025-04-25T03:01:59.000Z ## Abstract The dynamics of predator-prey systems influenced by intra-specific competition and additional food resources have increasingly become a subject of rigorous study in the realm of mathematical biology. In this study, we consider an additional food provided prey-predator model exhibiting Holling type-III functional response and the intra-specific competition among predators. We prove the existence and uniqueness of global positive solutions for the proposed model. We study the existence and stability of equilibrium points and further explore the possible bifurcations. We numerically depict the presence of Hysteresis loop in the system. We further study the global dynamics of the system and discuss the consequences of providing additional food. Later, we do the time-optimal control studies with respect to the quality and quantity of additional food as control variables by transforming the independent variable in the control system. We show that the findings of these dynamics and control studies emphasises the role of additional food and intra-specific competition in bio-control of pests. ## Recorded benchmark results A research result applies to its stated dataset, split, metric and evaluation configuration. Compare like-for-like settings, preserve the metric's unit and direction, and distinguish paper-reported results from independent reproduction. The best result recorded here is not a claim of exhaustive, current global coverage. ## Original sources and implementation [Original paper]() [PDF]()