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Consider the damped double-well potential model

$$

\ddot{x} - x + x^3 + \gamma\dot{x} = 0,

$$

where $\gamma$ is the damping coefficient.

This model has two fixed points at $(x,\dot{x}) = (1,0)$ and $(-1,0)$. In the phase plane $(x,\dot{x})$, determine the attraction basins of these fixed points. You can decide which $\gamma$ value to use (try to choose one which gives the best picture/graph). Note: the attraction basin of a fixed point is the set of initial points which go to the fixed as $t\to\infty$.