Dynamics of Approach-Avoidance Conflict during Exploration of Novel Objects in Mice*

Novelty poses a complex challenge to animals: in a potentially risky encounter with the unknown, they must balance exploration with safety. Indeed, many animals respond to novelty with a mix of curiosity and caution. Typically, when presented with conflicting incentives to approach and avoid a stimulus, animals oscillate between the two behaviors. Here, we reconstruct the phase space of oscillatory behaviors elicited by novel objects in mice from experimental data. We show that the mice's behavior in a 1D circular maze can be characterized as a 2D dynamical system of the form d²θ/dt²=F(θ,dθ/dt). Interestingly, the mice behave as though they experience a different "force" F near the object depending on whether they are moving toward or away from it. The dependence of F on velocity is inconsistent with a popular model of approach-avoidance conflict, according to which the appetitive and aversive aspects of a stimulus create overlapping motivational "potential fields", and F is the gradient of the summed potentials. Transitions between this and other types of exploratory behaviors require time-dependence of F.