Model for forest ecosystems based on quantum optimization

Abstract

This paper presents a mathematical model developed to describe the dynamics of forest ecosystems. The model is based on the principles of cross-diffusion, consider the interaction between two plant species in a forest environment. The model considers various parameters, like diffusion, growth and interaction coefficients and environmental capacities between species. Factors of influence of external conditions on each species of plants are also introduced. The differential equations are solved numerically using the finite difference method. This paper studies cross-diffusion dynamics by combining classical differential equations and quantum-inspired optimization techniques. The focus is on cross-diffusion processes, where populations interact through complex mechanisms of diffusion and reaction. The study uses a hybrid approach that combines classical methods for solving differential equations with quantum optimization, a quantum computing platform. Visualization of the results is presented in the form of 3D graphs reflecting the spatial distribution of plant populations in a forest ecosystem at various time steps. The resulting mathematical model and its visualization provide a tool for a deeper understanding of the influence of various factors on the dynamics of forest ecosystems. Analysis of such a model could be useful for predicting longterm changes in forests and developing sustainable forest management strategies.