Lotka-Volterra Modeling for Introducing Intraspecific Competition and Multi-Species Extension

The classical Lotka-Volterra (LV) model, while foundational, exhibits limitations by neglecting the influence of intraspecific competition within prey and predator populations on their own dynamics, and by restricting interactions to only two species. This study addresses these shortcomings. Firstly, we incorporate intraspecific competition terms into the LV equations and rigorously analyze the structure and stability of the resulting singular (equilibrium) solutions. Sensitivity analysis quantifies the impact of the intraspecific competition strength on key system parameters. Secondly, acknowledging the LV model's similarity in derivation to the logistic model, we construct a generalized multi-species LV model capable of representing complex ecological communities. Crucially, we develop a novel method utilizing Taylor's formula and transfer matrices to compute short-term solutions for this multi-species system. Collectively, this work significantly extends the classical LV framework, provides a computationally feasible approach for multi-species dynamics, and establishes new analytical perspectives on predator-prey interactions incorporating density-dependent feedback.