A simple model to account for the way in which two different animal species sometimes interact is the predator-prey model. If u(t) is the number of individuals in the predator species and v(t) the number of individuals in the prey species, then under suitable simplifying assumptions, the model is given by = 0.25u 0.01uv, u(0) = 80 = 0.01uv v, v(0) = 30. Use the fourth-order runge-kutta method with step-size h = 1 to approximate the solution at t =
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u(0) = 80 = 0.01uv v, v(0) = 30. Use the fourth-order runge-kutta method with step-size h = 1 to
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The Lotka–Volterra equations, also known as the predator–prey equations, are a pair of first-order nonlinear differential equations, frequently used to describe the dynamics of biological systems in which two species interact, one as a predator and the other as prey.
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