By Suli E., Mayers D.
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Extra resources for An Introduction to Numerical Analysis - Solutions
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.
An Introduction to Numerical Analysis - Solutions by Suli E., Mayers D.