Analytical Solutions of a Modified Predator-Prey Model through a New Ecological Interaction

Area of Science:

• Ecology
• Mathematical Biology
• Population Dynamics

Background:

• Predator-prey models are essential for predicting animal population dynamics.
• Sexual interaction during mating periods leads to predators feeding together, creating a two-predator, one-prey scenario.
• Existing models often do not fully capture the complexities of such group feeding behaviors.

Purpose of the Study:

• To present a nonlinear diffusive predator-prey model that incorporates the ecological interaction of two predators feeding on a single prey species.
• To analyze the influence of this specific interaction on predator and prey population dynamics.
• To provide analytical solutions for the presented dynamical system.

Main Methods:

• Development of a nonlinear diffusive predator-prey model.
• Analytical solution of the dynamical system using two distinct, reliable methods.
• Expression of solutions in terms of hyperbolic functions.

Main Results:

• Analytical solutions for the two-predator, one-prey model were successfully obtained.
• The solutions, presented using hyperbolic functions, predict the population dynamics.
• The biological relevance of these mathematical solutions within the ecological context was discussed.

Conclusions:

• The study successfully modeled a specific predator-prey interaction involving sexual behavior.
• Analytical solutions provide a quantitative understanding of population fluctuations in this scenario.
• The findings contribute to the refinement of ecological models for complex feeding interactions.