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 stars strong magnetic field close to the corotation radius (where the Keplerian frequency matches the stars 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.
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