Abstract
We describe a modification to our recent model of the action potential which introduces two additional equilibrium points. By using stability analysis we show that one of these equilibrium points is a saddle point from which there are two separatrices which divide the phase plane into two regions. In one region all phase paths approach a limit cycle and in the other all phase paths approach a stable equilibrium point. A consequence of this is that a short depolarizing current pulse will change an initially silent model neuron into one that fires repetitively. Addition of a third equation limits this firing to either an isolated burst or a depolarizing afterpotential. When steady depolarizing current was applied to this model it resulted in periodic bursting. The equations, which were initially developed to explain isolated triggered bursts, therefore provide one of the simplest models of the more general phenomenon of oscillatory burst discharge.
Reference19 articles.
1. Arrowsmith D. K. & Place C. M. 1982 Ordinary differential equations. London: Chapman & Hall:
2. A description of adaptation in excitable membranes. J. theor;Colding-Jorgensen M.;Biol.,1976
3. Prediction of repetitive firing behaviour from voltage clamp data on an isolated neurone soma
4. Control of a central pattern generator by an identified modulatory interneurone in Crustacea. II. Induction and modification of plateau properties in pyloric neurones. J. exp;Dickenson P. S.;Biol.,1983
5. Impulses and Physiological States in Theoretical Models of Nerve Membrane
Cited by
1479 articles.
订阅此论文施引文献
订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献