Dynamic mode decomposition based prediction method for diffusive Lotka-Volterra equation
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In this work, we propose a dynamic mode decomposition (DMD) based prediction method for diffusive Lotka-Volterra equations. To accommodate the multi-species structure of the model, we concatenate the solutions of all species into a single snapshot. Once the DMD modes are extracted, we can separate the modes of each species easily. While each species exhibits distinct mode shapes, they share identical eigenvalues, indicating that interspecies interactions are captured. Snapshot data are first generated using a finite difference method, and long-term predictions are then obtained via the DMD reconstruction. From these predictions, we reconstruct the species dominance indicator function, which classifies the dominant species at each spatial location. Numerical experiments demonstrate that the DMD based predictions for dominance indicator function achieves high accuracy while effectively reducing computational cost.
Abstract
In this work, we propose a dynamic mode decomposition (DMD) based prediction method for diffusive Lotka-Volterra equations. To accommodate the multi-species structure of the model, we concatenate the solutions of all species into a single snapshot. Once the DMD modes are extracted, we can separate the modes of each species easily. While each species exhibits distinct mode shapes, they share identical eigenvalues, indicating that interspecies interactions are captured. Snapshot data are first generated using a finite difference method, and long-term predictions are then obtained via the DMD reconstruction. From these predictions, we reconstruct the species dominance indicator function, which classifies the dominant species at each spatial location. Numerical experiments demonstrate that the DMD based predictions for dominance indicator function achieves high accuracy while effectively reducing computational cost.