By J. H. Davenport
This e-book nonetheless is still the simplest advent to computing device algebra, catering to either the newbie and the skilled natural mathematician and desktop scientist. This up-to-date moment version presents a finished overview, and includes very good references to primary papers and labored examples. as well as being a common textual content at the topic, the e-book comprises an appendix describing using one specific algebra system-REDUCE.
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This publication nonetheless continues to be the easiest advent to computing device algebra, catering to either the newbie and the skilled natural mathematician and desktop scientist. This up to date moment variation presents a complete overview, and includes very good references to basic papers and labored examples.
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Extra resources for Computer Algebra: Systems and Algorithms for Algebraic Computation
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.
Computer Algebra: Systems and Algorithms for Algebraic Computation by J. H. Davenport