Ponente
Descripción
Since the Industrial Revolution, humanity has been intensifying the burning of fossil fuels and as a consequence, the average temperature on Earth has been increasing. The 20th century was the warmest and future prospects are not favorable, that is, even higher temperatures are expected. This thermal imbalance has driven drastic changes in weather patterns across the globe, such as heat waves and cold spells, severe droughts, torrential rains and storms, as well as floods and landslides.
The survival of different species of animals and plants is more challenging than ever. This demonstrates the importance of studies on the subject, mainly to predict possible environmental, social and economic consequences. The objective of this work was to investigate the impact of advective and diffusive terms on the population dynamics of prey and predators, described by a Lotka-Volterra type model (Murray, J. D. Mathematical Biology: I. An Introduction. Springer-Verlag, New York, 2002), with three species, whose populations are spatially distributed in different locations. They are two prey species, competing with each other for the same resources, and a predator of both. In the proposed model, advective parameters describe the movement of populations in the spatial domain, and diffusion coefficients describe the spread of individuals. The discretizations of the equations were performed using finite difference schemes (FDS), namely, the Upwind method for the advective term, a centered FDS for the diffusive term, and an advanced FDS for the time derivative. The computational tests were implemented in Python, maintaining spatial and temporal spacing choices that satisfy the Courant, Friedrichs and Lewy (CFL) stability criteria and the diffusive term criterion (Thomas, J. W. Numerical Partial Differential Equations: Finite Difference Methods. Springer-Verlag, New York, 1995). Based on values from literature for the parameters related to the interaction between species (Liu, P.-P. An analysis of a predator-prey model with both diffusion and migration, Mathematical and Computer Modelling, 51:1064-1070, 2010), scenario simulations were executed. The solutions obtained allowed us to visualize different situations that can occur, for example, because a certain species needs to move further to find food and/or needs to spread its individuals in an attempt to survive. Therefore, the results showed that the inclusion of advective and diffusive terms enables the modeling of species displacement, revealing the different dynamics that occur in regions where interspecific encounters occur or not.