  Some accreting neutron stars and young stars show unexplained episodic flares
in the form of quasi-periodic oscillations or recurrent outbursts. In a series
of two papers we present new work on an instability that can lead to episodic
outbursts when the accretion disc is truncated by the star's strong magnetic
field close to the corotation radius (where the Keplerian frequency matches the
star's rotational frequency). In this paper we outline the physics of the
instability and use a simple parameterization of the disc-field interaction to
explore the instability numerically, which we show can lead to repeated bursts
of accretion as well as steady-state solutions, as first suggested by Sunyaev
and Shakura. The cycle time of these bursts increases with decreasing accretion
rate. These solutions show that the usually assumed `propeller' state, in which
mass is ejected from the system, does not need to occur even at very low
accretion rates.
