2. Consider the system described by the following differential equation x = rx - sinx (a) Find all fixed points for this

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2 Consider The System Described By The Following Differential Equation X Rx Sinx A Find All Fixed Points For This 1 (97.11 KiB) Viewed 34 times

2. Consider the system described by the following differential equation x = rx - sinx (a) Find all fixed points for this system as a function of r. (4 marks) (b) Determine the stability of all fixed points. (4 marks) (c) Plot the bifurcation diagram for -∞ <r <∞, and indicate the stability of the various branches of fixed points. (2 marks) (d) For the case r = 0, find and classify all the fixed points. (2 marks) (e) As r decreases from ∞ to 0, classify all the bifurcation that occurs. (4 marks) (f) As r increases from -∞ to 0, classify all the bifurcation that occurs. (4 marks) (Total: 20 marks)