The evolutions of the transition rate | a ˙ + ( t ) | (red thin lines), | a ˙ − ( t ) | (blue thin lines) and their upper bound functions Γ ( t ) (black lines). The control parameters are α 0 = 0.2 , α 1 = 0.2 , ω = 0.02 ω 0 , (a) ν = 0.04 ω 0 and (b) ν = 0.01 ω 0 , with the initial probabilities p ± ( 0 ) = 0.5 .