Problem Statement: Consider the model of nonlinear dynamics defined by an initial value problem governed by the following ordinary differential equation: ü−e(1-rû²)ù+α(1+ ßu² ) u = F₁ cost with parameters a, ß, e, %, and Fo, along with initial conditions (0) = 4, and (0)=%- Investigate the character of this problem and its solutions using both analytical and numerical methods, including those discussed in Module 2 of the course. Several subsets of the general problem, formed by setting some of the parameters to zero, may be investigated as part of your study. An emphasis on interesting aspects of the problem is encouraged. Prepare a report detailing your methods, approaches and findings, while citing all references used. Submit your report as a single pdf file through the UB Learns system. You may work individually or in a group of two students. For project groups, please submit only a single report, but indicate both names on the cover page.

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Problem Statement: Consider the model of nonlinear dynamics defined by an initial value problem governed by the following ordinary differential equation: ü−e(1-rû²)ù+α(1+ ßu² ) u = F₁ cost with parameters a, ß, e, %, and Fo, along with initial conditions (0) = 4, and (0)=%- Investigate the character of this problem a