With this circuit you can get a constant frequently changing duty cycle as you want.
Very stable. The 555 output is integrated to make a d.c. level that attack a driver with high input impedance. Right diode has an action like a trigger. Under 0.7v don't light.
The output... As you want.
Move potentiometer cursor to change power curve.
R1 = R2 = 2'5℅P1
D1 = D2 = 2N4148
C1 = Japanese
All R -> High PRECISION <1% if it's possible
555 -> NE555, SA555, SE555
