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Lynx eat snowshoe hares and snowshoe hares eat woody plants like willows. Suppose that, in the absence of hares, the willow population will grow exponentially and the lynx population will decay exponentially. In the absence of lynx and willow, the hare population will decay exponentially. If $ L(t), H(t), $ and $ W(t) $ represent the populations of these three species at time $ t, $ write a system of differential equations as a model for their dynamics. If the constants in your equation are all positive, explain why you have used plus or minus signs.
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Calculus 2 / BC
Chapter 9
Differential Equations
Section 6
Predator-Prey Systems
Campbell University
University of Michigan - Ann Arbor
Boston College
Lectures
13:37
A differential equation is a mathematical equation for an unknown function of one or several variables that relates the values of the function itself and its derivatives of various orders. An ordinary differential equation (ODE) is a differential equation containing one or more derivatives of a function and their rates of change with respect to the function itself; it can be used to model a wide variety of phenomena. Differential equations can be used to describe many phenomena in physics, including sound, heat, electrostatics, electrodynamics, fluid dynamics, elasticity, quantum mechanics, and general relativity.
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it was for So we know that means we eat snowshoe hares and a social hairs eat, we lose or care. So there to situations The first one says, um, that hairs are not president. So this is true. Then we want to see how the links and wills well, how the wings be here. So you could write down the director derivative off the wills respected Time is going to equal to que times w minus k times. So this is true because the here the Williams will grow exponentially. That's why it's a positive. It w and then the limbs will dig caves full. Actually, that's really we have the negative K times. So Ah, the second situation is that the links and there would low are not present. This is true. We want to see how the, um Harris change with time so we could write down derivative off h respected time. And then h is, um here's so what will happen to them? Well, we know that the hair publisher will be care exponentially so we could write need okay times each. And that is a
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