Equações a diferenças e a dinâmica populacional

Abstract

The main objective of this work was to present discrete mathematical models developed with difference equations. Specifically, we analyzed the Ricker model and the logistic model, both discrete nonlinear models formed by a difference equation. Initially, we present the most important theoretical concepts about logistic and Ricker models, such as equilibrium solutions, stability analysis and qualitative behavior change as a function of a parameter. For this, we found solutions through numerical simulations developed with Matlab software. For such models, we obtain different growth scenarios, depending on the intrinsic growth rate considered. We observed from monotonic growth to the equilibrium point of population persistence, to aperiodic solutions, characterizing chaotic behavior. We conclude that apparently simple discrete models can present several dynamic patterns quite distinct from each other.