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(Solved): 5. For the following dynamic system x=rxln(1+x), find the critical value of r that a bifurcat ...
![5. For the following dynamic system
\[
\dot{x}=r x-\ln (1+x),
\]
find the critical value of \( r \) that a bifurcation occurs](https://media.cheggcdn.com/media/351/351f199c-a9c1-47db-b50c-724319f39be3/phpk0UGHH)
5. For the following dynamic system find the critical value of that a bifurcation occurs and sketch the bifurcation diagram. [Note that the curve in the bifurcation diagram can be either an exact one based on nonlinear function or an approximate one from normal form]