Closed - loop stabilization of the Jamming Avoidance Response 1 reveals its locally unstable and globally nonlinear dynamics

The Jamming Avoidance Response, or JAR, in the weakly electric fish has been analyzed at all levels of organization, from 9 whole-organism behavior down to specific ion channels. Nevertheless, a parsimonious description of the JAR behavior in terms of 10 a dynamical system model has not been achieved at least in part due to the fact that “avoidance” behaviors are both intrinsically 11 unstable and nonlinear. We overcame the instability of the JAR in Eigenmannia virescens by closing a feedback loop around the 12 behavioral response of the animal. Specifically, the instantaneous frequency of a jamming stimulus was tied to the fish’s own 13 electrogenic frequency by a feedback law. Without feedback, the fish’s own frequency diverges from the stimulus frequency, but 14 appropriate feedback stabilizes the behavior. After stabilizing the system, we measured the responses in the fish’s instantaneous 15 frequency to various stimuli. A delayed first-order linear system model fit the behavior near the equilibrium. Coherence to white 16 noise stimuli together with quantitative agreement across stimulus types supported this local linear model. Next, we examined the 17 intrinsic nonlinearity of the behavior using clamped-frequency-difference experiments to extend the model beyond the neighborhood 18 of the equilibrium. The resulting nonlinear model is composed of competing motor return and sensory escape terms. The model 19 reproduces responses to step and ramp changes in the difference frequency (dF) and predicts a ’snap-through’ bifurcation as a 20 function of dF that we confirmed experimentally. 21