Fig. 2. Dynamics of homing using (A) Eqn 3 and (B) Eqn 4. The horizontal axis shows the animal's orientation, ; the vertical axis shows the animal's rate of turn d/dt, where (x,y) is the geocentric rectangular home vector (HV) and (r,) is the geocentric polar HV (see Fig. 1). This example shows the case where (A) x>0, y=2x and, in equivalence, (B) =tan^–12=1.107. Both schemes lead to one stable and one unstable equilibrium heading with the same respective values.