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Stochastic Investigation of a Limit Cycle System: Generalized Lotka-Selkov Reaction
Abstract
For a special reaction scheme, (--> Y, Y --> X (autocatalytic), X --> ) which is a generalization of the well-known schemes of Lotka and Selkov, the transition to a limit cycle regime is investigated. Analogies to phase transitions of first and second kind are studied. Analytical approximations for the solutions of the master equations are given and especially the phase fluctuations in the case of limit cycles are discussed.
... Note that by including quadratic terms into F (X), the passive system can be converted into an active one [10,38,39]. ...
First we discuss some early work of Ulrike Feudel on structure formation in nonlinear reactions including ions and the efficiency of the conversion of chemical into electrical energy. Then we give some survey about energy conversion from chemical to higher forms of energy like mechanical, electrical and ecological energy. We consider examples of energy conversion in several natural processes and in some devices like fuel cells. Further, as an example, we study analytically the dynamics and efficiency of a simple "active circuit" converting chemical into electrical energy and driving currents which is roughly modeling fuel cells. Finally we investigate an analogous ecological system of Lotka - Volterra type consisting of an "active species" consuming some passive "chemical food". We show analytically for both these models that the efficiency increases with the load, reaches values higher then 50 percent in a narrow regime of optimal load and goes beyond some maximal load abrupt to zero.
This thoroughly updated version of the German authoritative work on self-organization has been completely rewritten by internationally renowned experts and experienced book authors to also include a review of more recent literature. It retains the original enthusiasm and fascination surrounding thermodynamic systems far from equilibrium, synergetics, and the origin of life, representing an easily readable book and tutorial on this exciting field. The book is unique in covering in detail the experimental and theoretical fundamentals of self-organizing systems as well as such selected features as random processes, structural networks and multistable systems, while focusing on the physical and theoretical modeling of natural selection and evolution processes. The authors take examples from physics, chemistry, biology and social systems, and include results hitherto unpublished in English. The result is a one-stop resource relevant for students and scientists in physics or related interdisciplinary fields, including mathematical physics, biophysics, information science and nanotechnology.
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