Predator-prey analitycal dinamics behavior using normal form method

Normal form theory is one important tool in local analysis of nonlinear dynamical systems near an equilibrium point. In this paper a systematic procedure based on normal form theory is proposed to investigate nonlinear effects arising from the perturbation model of the predator-prey dynamic model of Lotka Volterra. Using this method, a second-order model of the predator-prey is proposed in which weak system nonlinearities are explicitly represented. Analytical expressions are then obtained that provide approximate solutions to system performance near a singularity, and techniques for interpreting these solutions in terms of modal functions are given. New insights into the nature of nonlinear oscillations are offered and criteria for characterizing nonlinear effects are discussed. Attention is also focused on assessing the effect of system stress on nonlinear dynamic performance.