A logistic model describes population growth that is initially exponential but slows down as the population reaches a maximum sustainable size, known as the carrying capacity. The logistic model is expressed using a first-order nonlinear differential equation.
In polar coordinates, the derivative involves both the radial \(r\) and angular \(\theta\) components. The rate of change of the Cartesian coordinates \(x\) and \(y\) is calculated using the product rule, accounting for changes in both \(r\) and \(\theta\) with respect to time.
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