Chaos in a Generalized Perturbed Lotka–Volterra Model

In this paper we investigate the chaos of a generalized perturbed Lotka–Volterra model based on considerations by other studies used in the literature. The model, containing N number of free parameters, could be of interest to specialists working in the fields of biological applications, chemistry, reaction kinetics, biostatistics, games theory, etc. With a specially developed software product, we generate the Melnikov equation M(t)=0 and examine all its zeros. This opens up an opportunity for the researcher to correctly understand and formulate the classical Melnikov criterion for the possible occurrence of chaos in the dynamical system. Several simulations are composed. We also demonstrate some specialized modules for investigating the dynamics of the proposed model. We further develop our model using the exponential form of the sine function. Thus, the perturbation can be interpreted as a term dependent on the characteristic function of a probability distribution. Although the original formulation leads to a distribution stated on a discrete domain, we can easily generalize the results for arbitrary distributions. Some particular examples are provided.