1. A brief discussion of all terms in each system. For example, what does the co
ID: 3122733 • Letter: 1
Question
1. A brief discussion of all terms in each system. For example, what does the coefcient to the x term in equation for dx/dt represent? Which system is cooperative and which is competitive?
2. For each system, determine all relevant equilibrium points and analyze the behavior of solutions whose initial conditions satisfy either x0 = 0 ory0 = 0. Determine the curves in the phase plane along which the vector eld is either horizontal or vertical. Which way does the vector eld point along these curves?
3. For each system describe all possible population evolution scenarios using the phase portrait as well as x(t)- and y(t)-graphs. Give special attention to the interpretation of the computer output in terms of the long-term behavior of the populations.
Systems:
Pair (1):
A.dx dt = 5x +2xy
dy dt = 4y+3xy
B.dx dt =6x x^2 4xy
dy dt =5y2xy2y^2
Pair (2):
A. dx dt = 3x +2xy
dy dt = 5y+3xy
B.dx dt =5x x^2 3xy
dy dt =8y3xy3y^2
Explanation / Answer
Here x is called input variable that is differentiated with respect to another variable t. Now in real world, a competitive system is one where both entities are harmed by each other on interaction and cooperative system is one where both are benefitted with each other.
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