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Fig. 9. Typical results for the position response of the bees. We obtained the hypothetical variation in position of the bees (z_b, red lines) according to Eqn 7. The bold broken green lines represent the visual stripe position (z_v). We focused on the amplitudes of z_b (A_{z_b}) and z_v (A_{z_v}), and the phase differences between z_b and z_v ( ${theta}$ ). (A) When ${omega}$ =0.9 Hz (5.6 rad s^-1), A_{z_b} is larger than A_{z_v}, and ${theta}$ is larger than -180°. (B) When ${omega}$ =1.8 Hz (11 rad s^-1), A_{z_b} is a little smaller than A_{z_v}, and ${theta}$ is larger than -180°. (C) When ${omega}$ =3.6 Hz (22 rad s^-1), A_{z_b} becomes much smaller than A_{z_v}, and ${theta}$ is approximately -180°. (D) When ${omega}$ =7.4 Hz (46 rad s^-1), the oscillation in z_b is hardly perceptible. The value of ${theta}$ is, in fact, much smaller than -180°.

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