Technical note: stable and unstable reactors

It is well known that a reactor is stable if the core reactivity decreases with the core power. This is the case for many types of reactors, including the PWR. However, this was not the case for the RBMK (Reaktor Bolshoy Moshchnosti Kanalniy) which could be unstable at low power. What does it mean precisely? By using a 2 × 2 system of non-linear ordinary differential equations we show that naturally (i.e. without using the control rods), with the same reactivity injection, if the initial power is lowered, then the final power may be higher, which is a rather unusual behaviour.