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) $\left\{ \begin{array} { l } \frac { d x } { d t } = - 0.01 x \\\frac { d y } { d t } = - 0.02 y\end{array} \right.$

---

Definitions:

Gift

A transfer of property or funds from one person to another without any expectation or requirement of payment or compensation.

Intangible

Assets or properties that do not have physical substance, such as patents, copyrights, or brand reputation.

Material Facts

Important facts that could influence a decision maker’s conclusion or outcome in a legal, financial, or commercial context.

Insurer

A company or entity that provides financial protection against specified risks in return for premiums.