Motivation modulates behaviour depending upon contextual and internal cues. Like animals, successful artificial agents must implement different behavioural strategies in order to satisfy dynamical needs. Such causal factors emerge from internal homeostatic or allostatic processes, as well as from external stimuli or threats. However, when two or more needs coalesce, a situation of motivational conflict ensues. In this work we present a four-stage dynamical framework for the resolution of motivational conflict based upon principles from dynamical systems and statistical mechanics. As a central mechanism for the resolution of conflict we propose the use of potentials with multiple wells or minima. This model leads to behavioural switching either by means of a bifurcation or by the stochastic escape from one of the wells. We present analytical and simulation results that reproduce known motivational conflict phenomena observed in the study of animal behaviour, in the case of two conflicting motivations.