- #1
mathboy20
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Hi
I need help intepreting the following.
Given Lotka-Volterra model system
\begin{array}{cc} x'_1 = (a-bx_2)x_1 \\ x'_2 = (cx_1 -d) x_2\end{array}
Look at the system on the open 1.Quadrant K; where a,b,c,d are all positive constants.
Show that the system is integratable, which supposedly implies that there exist a C^1-function F:U \rightarrow \mathbb{R} where U \subseteq K is open, and close in K.
According to my professor "close" implies that for every point in K, there exist a sequence of socalled "limitpoints", who's elements belongs to K. Also as a consequence of "close" \nabla F \neq 0 for all x \in U, and F is constant on all trajectories of the system.
What is my first step here? Do I prove that there exist a solution for the system only in K?
Sincerley Yours
Mathboy20
I need help intepreting the following.
Given Lotka-Volterra model system
\begin{array}{cc} x'_1 = (a-bx_2)x_1 \\ x'_2 = (cx_1 -d) x_2\end{array}
Look at the system on the open 1.Quadrant K; where a,b,c,d are all positive constants.
Show that the system is integratable, which supposedly implies that there exist a C^1-function F:U \rightarrow \mathbb{R} where U \subseteq K is open, and close in K.
According to my professor "close" implies that for every point in K, there exist a sequence of socalled "limitpoints", who's elements belongs to K. Also as a consequence of "close" \nabla F \neq 0 for all x \in U, and F is constant on all trajectories of the system.
What is my first step here? Do I prove that there exist a solution for the system only in K?
Sincerley Yours
Mathboy20
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