By Shinji Doi, Junko Inoue, Zhenxing Pan, Kunichika Tsumoto (auth.)
Biological structures inherently own a lot ambiguity or uncertainty. Computational electrophysiology is the only region, from one of the gigantic and speedily becoming self-discipline of computational and structures biology, during which computational or mathematical types have succeeded. This ebook presents a pragmatic and speedy consultant to either computational electrophysiology and numerical bifurcation research. Bifurcation research is the most important device for the research of such hugely nonlinear organic platforms. Bifurcation thought presents how to learn the influence of a parameter swap on a method and to notice a severe parameter price whilst the qualitative nature of the approach alterations. integrated during this paintings are many examples of numerical computations of bifurcation research of assorted versions in addition to mathematical versions with diversified abstraction degrees from neuroscience and electrophysiology. This quantity will gain graduate and undergraduate scholars in addition to researchers in varied fields of science.
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Extra info for Computational electrophysiology: dynamical systems and bifurcations
These results are consistent with the above explanations on the super-critical Hopf bifurcation (Fig. 11). 51): PD C P D 1: 3 D . 54) is the sign of the nonlinear (cubic) term in thepfirst equation. Thus, this system has an unstable periodic orbit with an amplitude when < 0. 55) becomes P D C 3 . See the bifurcation diagram of Fig. 13. 4. 54). 41) is seemingly too simple to model and analyze real systems. The one-dimensional map, however, arises commonly from general ndimensional dynamical systems.
3), and Iext the current stimulus applied S.
This command solves or integrates differential equations from the final (last) value of previous solution. Thus we can obtain the approximate values of the stable equilibrium point. We can see these values by clicking on Sing pts and (G)o. File and Auto buttons create a new window such as Fig. 21 for bifurcation analysis using the AUTO. (Note that results of bifurcation analysis have already Fig. 21 The AUTO Window. Equilibrium points are drawn as a function of the parameter L. Thick and thin lines show stable and unstable equilibrium points, respectively.
Computational electrophysiology: dynamical systems and bifurcations by Shinji Doi, Junko Inoue, Zhenxing Pan, Kunichika Tsumoto (auth.)