Viewing topic: Nullclines

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  • Definition: Nullclines, sometimes called zero-growth isoclines, are encountered in a system of ordinary differential equations: x_1' = f_1(x_1, ... , x_n); x_2' = f_2(x_1, ... , x_n); ... ; x_n' = f_n(x_1, ... , x_n) where the ' here represents a derivative with respect to another parameter, such as time t. Nullclines are the geometric shape for which x_j'=0 for any j. The fixed points of the system are located where all of the nullclines intersect. In a two-dimensional linear system, the nullclines can be represented by two lines on a two-dimensional plot; in a general two-dimensional system they are arbitrary curves.

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