Diff Eq: Cooperative and Competitive Species
A. dx/dt= -5x+2xy B. dx/dt=6x-x^2-4xy
dy/dt= -4y+3xy dy/dt=5y-2xy-2y^2
Discuss the terms in each system, ie, what does the coefficient to the x term in x' represent, and which system is cooperative/competitive?
Determine all relevant equilibrium points and analyze behavior when x0=0 or y0=0. Determine the curves in the phase plan along which the vector field is either horizontal or vertical; which way does the vector field point along these curves?
Describe possible evolution scenarios.
Stacey Warren - Expert brainly.com
Hey! We 've verified this expert answer for you, click below to unlock the details :)
At vero eos et accusamus et iusto odio dignissimos ducimus qui blanditiis praesentium voluptatum deleniti atque corrupti quos dolores et quas molestias excepturi sint occaecati cupiditate non provident, similique sunt in culpa qui officia deserunt mollitia animi, id est laborum et dolorum fuga.
Et harum quidem rerum facilis est et expedita distinctio. Nam libero tempore, cum soluta nobis est eligendi optio cumque nihil impedit quo minus id quod maxime placeat facere possimus, omnis voluptas assumenda est, omnis dolor repellendus.
Itaque earum rerum hic tenetur a sapiente delectus, ut aut reiciendis voluptatibus maiores alias consequatur aut perferendis doloribus asperiores repellat.
I got my questions answered at brainly.com in under 10 minutes. Go to brainly.com now for free help!
Does anyone have time to review my thoughts as I work on my response?
In a cooperative system, the coefficient of x in the equation for dx/dt represents the reliance of the two species upon each other. The coefficient of y in the equation for dy/dt also represents this reliance. The greater the coefficient, the less valuable/critical one species is to the other; that is, a dx/dt coefficient of x closer to zero will have less reliance on the opposite species for continued growth.
EPs: A: (0,0) (-4/3,-3/2)
B: (0,0) (0, 5/2) (6,0) (2/3, 5/6)
For all cooperative systems, if either population starts at 0, the system behaves as an exponential decay system. This is logical, since species rely on each other for growth in a cooperative system.