Model development
Our starting point is the original one-dimensional Keller model37 for competitive running
$$\begin{aligned} {\dot{v}}(t) = -\dfrac{1}{\tau }v(t) + f(t), \end{aligned}$$
(1)
where v(t) is the runner velocity and the dot indicates a derivative with respect to time, f(t) is the positive force per unit mass exerted by the runner, assumed to be constant throughout the race, and \(\tau >0\) is a constant modeling the physiological resistances felt by the runner.
Attacker-defender dribble model. (a) Schematic illustration of the vector…
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