# 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} }

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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