Coherent Oscillations in Biological Systems I

Abstract

Abstract The concept of long range coherence in biological systems of Fröhlich and its physical basis as well as his general theoretical considerations leading to the brain wave model are reviewed. The importance of these ideas is stressed both, as a possible explanation of the increasing experimental results and as a starting point to allow a theoretical description of biological events. The brain wave model is studied in detail. All possible bifurcations and the stability of the steady states is considered. The existence, stability and direction of bifurcation of a stable limit cycle is proven. The system may exhibit different types of phase transitions when it is externally disturbed. Phase plane diagrams, arguments of catastrophe theory and approximations to the model equations give a qualitative description of the system's time behaviour. Correspondence between this limit cycle model and nerve impulse generating models is established.