Robust Persistence and Permanence of Polynomial and Power Law Dynamical Systems

@article{Brunner2018RobustPA,
  title={Robust Persistence and Permanence of Polynomial and Power Law Dynamical Systems},
  author={James D. Brunner and Gheorghe Craciun},
  journal={SIAM J. Appl. Math.},
  year={2018},
  volume={78},
  pages={801-825}
}
  • James D. Brunner, Gheorghe Craciun
  • Published 2018
  • Computer Science, Mathematics
  • SIAM J. Appl. Math.
  • A persistent dynamical system in $\mathbb{R}^d_{> 0}$ is one whose solutions have positive lower bounds for large $t$, while a permanent dynamical system in $\mathbb{R}^d_{> 0}$ is one whose solutions have uniform upper and lower bounds for large $t$. These properties have important applications for the study of mathematical models in biochemistry, cell biology, and ecology. Inspired by reaction network theory, we define a class of polynomial dynamical systems called tropically endotactic. We… CONTINUE READING

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