A Game Theoretic Approach to Sustainizability Over Sets and its application to a multi-species population model
<|reference_start|>A Game Theoretic Approach to Sustainizability Over Sets and its application to a multi-species population model: In this work, a theorem is first proved which presents a game theoretic formulation of a necessary and sufficient sustainizability over a set condition for a general system described by ordinary differential equations (ODEs). Then, two additional theorems are proved for the n-species Gause-Lotka-Volterra (GLV) population model, establishing necessary and sufficient sustainability and sustainizability conditions over rectangular sets. Three case studies on the May-Leonard, 3-species, GLV model are then presented to illustrate the power of the above Theorems. In two of these case studies (2 and 3), it is shown that a particular instance of the 3-species, GLV model is unsustainable but sustainizable through allowable action.<|reference_end|>
@article{manousiouthakis2024a,
    title={A Game Theoretic Approach to Sustainizability Over Sets and its
  application to a multi-species population model},
    author={Ioannis V. Manousiouthakis (Hydrogen Engineering Research Company, LLC
  (H-E-R-C, LLC), Los Angeles, U.S.A), Vasilios I. Manousiouthakis (Hydrogen
  Engineering Research Consortium (HERC), University of California at Los
  Angeles)},
    journal={arXiv preprint arXiv:2403.08981},
    year={2024},
    archivePrefix={arXiv},
    eprint={2403.08981},
    primaryClass={math.OC cs.SY eess.SY nlin.CD}
}