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Stability analysis of this bi-gene regulation network is also presented based on parameter bifurcations.
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Based on two-parameter bifurcation analysis, we determined the combinations of sodium conductance ḡNa and potassium conductance ḡK required to give repetitive spiking at different stimulus thresholds.
13408_2015_19_MOESM1_ESM.pdf Full one parameter bifurcation diagrams.
Based on several two-parameter bifurcation diagrams, several parameters affecting the Hopf bifurcation are then discussed.
Based on (13), two-parameter bifurcation diagrams of K1 against other model parameters can be set up. Figure 5a illustrates on the K1 vs. n1 plane, regions of stable and oscillatory dynamics, separated by the K1thresh curve.
For the latter one, the nonlinear stability based on the bifurcation theory is analysed.
Traditionally, this analysis is based on sensitivity and bifurcations analysis; however, these tools are rather limited, due to their inability to take into account multiple simultaneous parameter variations.
Rinzel [17] introduced a scheme for classifying bursting mechanisms based on the bifurcation structure of the so-called fast subsystem where the slow variable is treated as a parameter.
The methodological tool is based on the bifurcation analysis of the structure Reactor/ Separation/ Recycle.
These results are what would be expected based on the bifurcation analysis.
In this article, based on attractor bifurcation theory we obtain the following results.
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