Consider an animal that forages in a field, which we will model as a flat 2-dimensional...

 

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Consider an animal that forages in a field, which we will model as a flat 2-dimensional space. The movement dynamics of the animal are given by the following linear system of ODES where dx dt A = (a) Find the nullclines of this system. (b) Determine the direction field on the nullclines. = Az (c) Sketch the phase plane, showing the direction field on the nullclines. (d) By considering the trace and determinant of A, fully classify the stability of the origin (hint: don't just say it is stable or unstable...). (e) Describe the movement of the animal. Consider an animal that forages in a field, which we will model as a flat 2-dimensional space. The movement dynamics of the animal are given by the following linear system of ODES where dx dt A = (a) Find the nullclines of this system. (b) Determine the direction field on the nullclines. = Az (c) Sketch the phase plane, showing the direction field on the nullclines. (d) By considering the trace and determinant of A, fully classify the stability of the origin (hint: don't just say it is stable or unstable...). (e) Describe the movement of the animal.