Stable feedback models for electrosensory filtering in mormyrid fish

We analyze a mathematical model for an adaptive mechanism in the electrosensory system of mormyrid weakly electric fish. Adaptive sensory filtering of electrosensory signals is regulated by spike-timing dependent plasticity using an asymmetric learning rule. We investigate a nonlinear control theoretic model and study the conditions on the learning rule that guarantee the existence of a globally stabilizing feedback law. Stability is necessary for optimal novelty detection in sensing environmental electrical sources. The model covers both the constant and variable spiking threshold cases. The results show that feedback control of synaptic plasticity is globally stable in this adaptive sensory system.