An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems

Gheorghe Craciun; Jiaxin Jin; Polly Y. Yu

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arXiv · 1812.06214

An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems

Gheorghe Craciun·Jiaxin Jin·Polly Y. Yu

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Abstract

Very often, models in biology, chemistry, physics, and engineering are systems of polynomial or power-law ordinary differential equations, arising from a reaction network. Such dynamical systems can be generated by many different reaction networks. On the other hand, networks with special properties (such as reversibility or weak reversibility) are known or conjectured to give rise to dynamical systems that have special properties: existence of positive steady states, persistence, permanence, and (for well-chosen parameters) complex balancing or detailed balancing. These last two are related to thermodynamic equilibrium, and therefore the positive steady states are unique and stable. We describe a computationally efficient characterization of polynomial or power-law dynamical systems that can be obtained as complex-balanced, detailed-balanced, weakly reversible, and reversible mass-action systems.

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BibTeX RIS

Gheorghe Craciun, Jiaxin Jin, Polly Y. Yu. 2018-12-15. An efficient characterization of complex-balanced, detailed-balanced, and weakly reversible systems. https://arxiv.org/abs/1812.06214

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