Consider the Non-Linear System $x ^ { \prime } = 1 - 2 x y , y ^ { \prime } = 2 x y - y$

question 41

Multiple Choice

Consider the non-linear system $x ^ { \prime } = 1 - 2 x y , y ^ { \prime } = 2 x y - y$ . The linearized system about the one critical point, $( 1 / 2,1 ) \text {, is } X ^ { t } = A X \text {, where } A =$

• A) \(\left( \begin{array} { l l }
• 2 & 1 \\
• 2 & 0
• \end{array} \right)\)
• B) \(\left( \begin{array} { c c }
• 2 & - 1 \\
• 2 & 0
• \end{array} \right)\)
• C) \(\left( \begin{array} { c c }
• - 2 & - 1 \\
• 2 & 0
• \end{array} \right)\)
• D) \(\left( \begin{array} { l l }
• - 2 & 1 \\
• - 2 & 0
• \end{array} \right)\)
• E) \(\left( \begin{array} { c c }
• - 2 & - 1 \\
• - 2 & 0
• \end{array} \right)\)

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Definitions:

Luteal Phase

Portion of the menstrual cycle extending from the time of formation of the corpus luteum after ovulation to the time when menstrual flow begins; usually 14 days in length; also called secretory phase.

Blood Hormone Levels

The concentration of hormones within the bloodstream, which can affect various bodily functions and health conditions.

GnRH

Gonadotropin-releasing hormone, a hormone responsible for the release of follicle-stimulating hormone (FSH) and luteinizing hormone (LH) from the pituitary gland.

FSH

Follicle Stimulating Hormone, a gonadotropin involved in the regulation of reproductive processes.