Diff Eq: Cooperative and Competitive Species System: 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.

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Diff Eq: Cooperative and Competitive Species System: 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.

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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.

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