Theoretical Analysis of Discreteness-Induced Transition in Autocatalytic Reaction Dynamics
arXiv:1403.6222 · doi:10.1103/PhysRevE.91.022707
Abstract
Transitions in the qualitative behavior of chemical reaction dynamics with a decrease in molecule number have attracted much attention. Here, a method based on a Markov process with a tridiagonal transition matrix is applied to the analysis of this transition in reaction dynamics. The transition to bistability due to the small-number effect and the mean switching time between the bistable states are analytically calculated in agreement with numerical simulations. In addition, a novel transition involving the reversal of the chemical reaction flow is found in the model under an external flow, and also in a three-component model. The generality of this transition and its correspondence to biological phenomena are also discussed.
arXiv comment7 pages, 4 figures
References in corpus (10)
- Predator-prey cycles from resonant amplification of demographic stochasticity
- The Importance of Being Discrete - Life Always Wins on the Surface
- Noise-Induced Bistable States and Their Mean Switching Time in Foraging Colonies
- Fluctuation-driven Turing patterns
- Transitions Induced by the Discreteness of Molecules in a Small Autocatalytic System
- Molecular Discreteness in Reaction-Diffusion Systems Yields Steady States Not Seen in the Continuum Limit
- Noise-induced metastability in biochemical networks
- Transition Phenomena Induced by Internal Noise and Quasi-absorbing State
- Alteration of Chemical Concentrations through Discreteness-Induced Transitions in Small Autocatalytic Systems
- Discreteness-induced Transition in Catalytic Reaction Networks
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