How to figure out the type of the bifurcation in a dynamical system? - MathOverflow most recent 30 from http://mathoverflow.net 2013-06-19T05:28:56Z http://mathoverflow.net/feeds/question/16588 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/16588/how-to-figure-out-the-type-of-the-bifurcation-in-a-dynamical-system How to figure out the type of the bifurcation in a dynamical system? kamran 2010-02-27T11:28:56Z 2010-02-28T23:14:31Z <p>Suppose we have a dynamical system </p> <p>$\dot{x} = f(x,r)$ </p> <p>in which x is a state variable and r is a bifurcation parameter. How to figure out which kind of bifurcation(s) (e.g. saddle-node, transcritical, pitchfork, hopf and etc) the system undergoes?</p> <p>Edit 1: consider the space as 1D or 2D.</p> http://mathoverflow.net/questions/16588/how-to-figure-out-the-type-of-the-bifurcation-in-a-dynamical-system/16634#16634 Answer by Thomas Sauvaget for How to figure out the type of the bifurcation in a dynamical system? Thomas Sauvaget 2010-02-27T20:53:37Z 2010-02-27T20:53:37Z <p>It depends: if you know $f$ explicitely then working out critical points and normal forms will tell you so, otherwise you'd have to use a specialized program. Have a look at <a href="http://www.scholarpedia.org/article/Bifurcations" rel="nofollow">this scholarpedia article</a> and the other articles, books and programs mentionned there (start with <a href="http://www.scholarpedia.org/article/Saddle-node_bifurcation" rel="nofollow">saddle-node</a>) .</p>