تقرير
Non-normality and non-monotonic dynamics in complex reaction networks
| العنوان: | Non-normality and non-monotonic dynamics in complex reaction networks |
|---|---|
| المؤلفون: | Nicolaou, Zachary G., Nishikawa, Takashi, Nicholson, Schuyler B., Green, Jason R., Motter, Adilson E. |
| المصدر: | Phys. Rev. Research 2, 043059 (2020) |
| سنة النشر: | 2020 |
| المجموعة: | Condensed Matter Nonlinear Sciences Physics (Other) Quantitative Biology |
| مصطلحات موضوعية: | Nonlinear Sciences - Adaptation and Self-Organizing Systems, Condensed Matter - Disordered Systems and Neural Networks, Physics - Chemical Physics, Quantitative Biology - Quantitative Methods |
| الوصف: | Complex chemical reaction networks, which underlie many industrial and biological processes, often exhibit non-monotonic changes in chemical species concentrations, typically described using nonlinear models. Such non-monotonic dynamics are in principle possible even in linear models if the matrices defining the models are non-normal, as characterized by a necessarily non-orthogonal set of eigenvectors. However, the extent to which non-normality is responsible for non-monotonic behavior remains an open question. Here, using a master equation to model the reaction dynamics, we derive a general condition for observing non-monotonic dynamics of individual species, establishing that non-normality promotes non-monotonicity but is not a requirement for it. In contrast, we show that non-normality is a requirement for non-monotonic dynamics to be observed in the R\'enyi entropy. Using hydrogen combustion as an example application, we demonstrate that non-monotonic dynamics under experimental conditions are supported by a linear chain of connected components, in contrast with the dominance of a single giant component observed in typical random reaction networks. The exact linearity of the master equation enables development of rigorous theory and simulations for dynamical networks of unprecedented size (approaching $10^5$ dynamical variables, even for a network of only 20 reactions and involving less than 100 atoms). Our conclusions are expected to hold for other combustion processes, and the general theory we develop is applicable to all chemical reaction networks, including biological ones. Comment: Software implementing our methods is available as a Github repository at https://github.com/znicolaou/ratematrix and an animated version of Fig. 1 is available at https://northwestern.box.com/s/otn3m2cov9gi3enht3r8jh5kjo9qnv6d |
| نوع الوثيقة: | Working Paper |
| DOI: | 10.1103/PhysRevResearch.2.043059 |
| URL الوصول: | http://arxiv.org/abs/2008.09616 |
| رقم الأكسشن: | edsarx.2008.09616 |
| قاعدة البيانات: | arXiv |
| DOI: | 10.1103/PhysRevResearch.2.043059 |
|---|