Recent research has highlighted that, in dynamical systems, especially when they are non-linear, small noises at the starting datum produce substantial changes in the long-term dynamics; this is connected with the so-called “complexity” and “deterministic chaos”. The stability theory aims to detect the asymptotic behavior of the system through the observation of its equilibrium points. A well-known example of non-linear system is the Lotka-Volterra model that describes the growth in an ecosystem, where only two species interact (“predators” and “prey”). This paper aims to show the adaptability of this model in the social-economical context, because it helps in explaining aspects of dichotomy not only in natural phenomena. Indeed, we also present the Goodwin model that extends the Lotka-Volterra model to the socio-economic context, and we apply it to Italy, using the R statistical software.