. (a) Sketch the bifurcation diagram for i = x + 2x + x, indicating the...
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. (a) Sketch the bifurcation diagram for i = µμx + 2x² + x³, indicating the stability of all solution branches and classifying any bifurcation points. (b) Find the value of a for which = -a + x + 2x² + x³ has a coalescence of saddle-node bifurcations, and find the values of z and u at the coalescence point. 18 (c) Hence, without doing further calculations, sketch the bifurcation diagrams, in- dicating the stability of all branches, when a is: (i) at the value for coalescence, (ii) close to the value for coalescence, giving an example where there are three saddle-node bifurcations, and an example where there is only one saddle- node bifurcation. [5] . (a) Sketch the bifurcation diagram for i = µμx + 2x² + x³, indicating the stability of all solution branches and classifying any bifurcation points. (b) Find the value of a for which = -a + x + 2x² + x³ has a coalescence of saddle-node bifurcations, and find the values of z and u at the coalescence point. 18 (c) Hence, without doing further calculations, sketch the bifurcation diagrams, in- dicating the stability of all branches, when a is: (i) at the value for coalescence, (ii) close to the value for coalescence, giving an example where there are three saddle-node bifurcations, and an example where there is only one saddle- node bifurcation. [5]
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Solution a To sketch the bifurcation diagram for i ux 2x2 13 we can start by looking at the stabilit... View the full answer
Related Book For
Differential Equations and Linear Algebra
ISBN: 978-0131860612
2nd edition
Authors: Jerry Farlow, James E. Hall, Jean Marie McDill, Beverly H. West
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