This Study Examines a Three-Species Interaction Model Representing the Dynamics Between Crops, Pests, and a Third Environmental Factor in Agriculture. The Model, Driven by Nonlinear Differential Equations, Explores How Crop Growth is Influenced by Carrying Capacity, Pest Predation, and Agricultural Interventions like Fertilization and Pesticides. Pest Dynamics Depend on Competition with Crops and Interactions with the Third Species, Which Could Signify Predators or Ecological Stressors. Through Equilibrium Analysis and Stability Assessment via Jacobian Matrices and Eigenvalues, the Model Offers Insights into Sustainable Farming and Pest Management. The Findings Contribute to Strategies for Ecological Balance, Optimal Yield, and Long-Term Agricultural Sustainability.