Delay-controlled reactions

• Published in: Physics letters. A Vol. 321; no. 4; pp. 205 - 215
• Main Authors: Trimper, Steffen, Zabrocki, Knud
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 09.02.2004
• Subjects: 05.70.Ln; 05.40.-a; 82.20.-w; 02.30.Ks; 87.23.Kg
• ISSN: 0375-9601; 1873-2429
• DOI: 10.1016/j.physleta.2003.12.045

When the entities undergoing a chemical reaction are not available simultaneously, the classical rate equation in the reaction-limited regime, 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 behavior, characterized by the existence of a time persistent solution. As an example we consider a single-species pair annihilation A+ A→∅ process combined with a spontaneous creation of particles ∅→ A.