Entrainment in nerve by a ferroelectric model (II): Quasi-periodic oscillation and the phase locking
✍ Scribed by Kotaro Shirane; Takayuki Tokimoto; Hiroyuki Kushibe
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 548 KB
- Volume
- 108
- Category
- Article
- ISSN
- 0167-2789
No coin nor oath required. For personal study only.
✦ Synopsis
A nonlinear state equation for membrane excitation can be simplified by Leuchtag's ferroelectric model which is applied to a chemical network theory. A dissipative structure of such a membrane is described by an equilibrium space, q3 + aq + b = 0, giving a cusp catastrophe, and the membrane is self-organized in the resting state under the condition, a < 0 (T < T,), where q corresponds to the membrane potential, and a and b imply dipole-dipole and dipole-ion interactions of channel proteins embedded in the membrane, respectively. As well known, a specific characteristic of nonlinear electrical phenomena in the membrane is a limit cycle arising through the entrainment by periodical stimuli or chaos. A phase transition between the equilibrium and the non-equilibrium states (a dissipative structure without the resting state) is described by a parameter giving the difference from thermal equilibrium. In this dynamic system, quasi-periodic oscillations which arise in periodic external fields and the phase locking, that is, entrainment, caused by changing 10 at w # wn (w, -the natural frequency of the membrane) are studied with parameters introduced into Zeeman's formulas of ir and I;.