Research Article A General Model of Population Dynamics Accounting for Multiple Kinds of Interaction Luciano Stucchi, 1,2 Juan Manuel Pastor, 2 Javier Garc´ ıa-Algarra , 3 and Javier Galeano 2 1 Universidad Del Pac´ ıfico, Lima, Peru 2 Complex Systems Group, E. T. S. I. A. A. B, Universidad Polit´ ecnica de Madrid, Madrid, Spain 3 Department of Engineering, Centro Universitario U-TAD, Las Rozas, Spain Correspondence should be addressed to Javier Galeano; javier.galeano@upm.es Received 13 May 2020; Accepted 22 June 2020; Published 24 July 2020 Guest Editor: Tongqian Zhang Copyright © 2020 Luciano Stucchi et al. is is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited. Population dynamics has been modelled using differential equations almost since Malthus times, more than two centuries ago. Basic ingredients of population dynamics models are typically a growth rate, a saturation term in the form of Verhulst’s logistic brake, and a functional response accounting for interspecific interactions. However, intraspecific interactions are not usually included in the equations. e simplest models use linear terms to represent a simple picture of the nature; meanwhile, to represent more complex landscapes, it is necessary to include more terms with a higher order or that are analytically more complex. e problem to use a simpler or more complex model depends on many factors: mathematical, ecological, or computational. To address it, here we discuss a new model based on a previous logistic-mutualistic model. We have generalized the interspecific terms (for antagonistic and competitive relationships), and we have also included new polynomial terms to explain any intraspecific interaction. We show that, by adding simple intraspecific terms, new free-equilibrium solutions appear driving a much richer dynamics. ese new solutions could represent more realistic ecological landscapes by including a new higher order term. 1. Introduction In the times of the coronavirus, many news on television and magazines try to explain how the size of the infected pop- ulation evolves, showing exponential plots of the infected populations over time. ese communications try to predict the time evolution of the size of this population in the future. Behind these predictions, there is always a differential equation model. ese polynomial models have linear terms, but to account for more complex interactions, they can add higher order terms, as quadratic, cubic, or even, analytically more complex functions, such as decreasing hyperbolic terms. e problem of choosing a complex or a simple model depends on the balance between properly representing nature and being able to understand the model response. In many cases, the simplest model may be enough to under- stand the benchmarks in the big picture, but sometimes, we need more complexity to represent significant aspects of our problem, and therefore, we need more complex and more difficult models. Finding the balance between simple and complex is a tricky problem, but how simple or complex should the model be? Let us try to answer this question in a population dynamics problem. In the study of population dynamics, Lotka [1] and Volterra [2] were the first ones to model trophic interactions in order to study predator-prey relationships within two (or more) populations: X 1 · � r 1 − b 12 X 2 ( X 1 , X 2 · � − r 2 + b 21 X 1 ( X 2 , (1) where b ij terms represent the rate of the interactions be- tween populations X i and X j and the r i represents their effective growth rates. In these equations, signs are Hindawi Complexity Volume 2020, Article ID 7961327, 14 pages https://doi.org/10.1155/2020/7961327