This circuit operates two LED strips in pulsing mode, i.e. one LED strip goes from off state, lights up gradually, then dims gradually, etc. while the other LED strip does the contrary.
Each strip can be made up from 2 to 5 LEDs at 9V supply. The two Op-Amps contained into IC1 form a triangular wave generator. The rising and falling voltage obtained at pin #7 of IC1 drives two complementary circuits formed by a 10mA constant current source (Q1, Q2 and Q5, Q6) and driver transistor (Q3 and Q6).
R4, R5 & C1 are the timing components: the total period can be varied changing their values. R7 & R8 vary the LEDs brightness.