In Each of the Given Systems, X and Y Are $\left\{ \begin{array} { l } \frac { d x } { d t } = - 0.01 x + 0.0002 x y \\\frac { d y } { d t } = - 0.2 y - 0.004 x y\end{array} \right.$

question 107

Essay

In each of the given systems, x and y are populations of two different species which are solutions to the differential equations. For each system, describe how the species interact with one another (for example, do they compete for the same resources, or cooperate for mutual benefit?) and suggest a pair of species that might interact in a manner consistent with the given system of equations.(a) $\left\{ \begin{array} { l } \frac { d x } { d t } = - 0.01 x + 0.0002 x y \\\frac { d y } { d t } = - 0.2 y - 0.004 x y\end{array} \right.$ (d) $\left\{ \begin{array} { l } \frac { d x } { d t } = 0.01 x ( 1 - 0.02 x ) + 0.1 x y \\\frac { d y } { d t } = 0.02 y ( 1 - 0.01 y ) + 0.01 x y\end{array} \right.$ (b) $\left\{ \begin{array} { l } \frac { d x } { d t } = 0.01 x + 0.0002 x y \\\frac { d y } { d t } = 0.2 y - 0.004 x y\end{array} \right.$ (e) $\left\{ \begin{array} { l } \frac { d x } { d t } = 0.08 x ( 1 - 0.0001 x ) - 0.002 x y \\\frac { d y } { d t } = - 0.02 y + 0.002 x y\end{array} \right.$ (c) $\left\{ \begin{array} { l } \frac { d x } { d t } = 0.01 x + 0.0002 x y \\\frac { d y } { d t } = 0.2 y + 0.004 x y\end{array} \right.$ (f) $\left\{ \begin{array} { l } \frac { d x } { d t } = - 0.01 x \\\frac { d y } { d t } = - 0.02 y\end{array} \right.$

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