Delay-Controlled Reactions
arXiv:cond-mat/0303067 · doi:10.1016/j.physleta.2003.12.045
Abstract
When the entities undergoing a chemical reaction are not available simultaneously, the classical rate equation of a reaction or, alternatively for the evolution of a population, should be extended by including non-Markovian memory effects. We consider the two cases of an external feedback, realized by fixed functions and an internal feedback originated in a self-organized manner by the relevant concentration itself. Whereas in the first case the fixed points are not changed, although the dynamical process is altered, the second case offers a complete new behaviour, characterized by the existence of a time persistent solution. Due to the feedback the reaction may lead to a finite concentration in the stationary limit even in case of a single-species pair annihilation process. We argue that the different cases are similar to a coupling of additive or multiplicative noises in stochastic processes.
18 pages, 3 figures
References in corpus (6)
- Noise-induced dynamics in bistable systems with delay
- Subdiffusion-limited reactions
- On solutions of a class of non-Markovian Fokker-Planck equations
- Time-delayed Spatial Patterns in a Two-dimensional Array of Coupled Oscillators
- Domain-size control by global feedback in bistable systems
- Criticality and oscillatory behavior in non-Markovian Contact Process