Nonlinear dynamics in free flight of an echolocating bat

Abstract

A mathematical model is proposed to describe the nonlinear dynamics of the echolocation behavior of a bat during free flight in an enclosed chamber. In the model, a bat dynamically controls its flight and pulse directions (φf and φp respectively), to avoid collision with multiple walls of the chamber; namely, the bat varies φf and φp repulsively from the closest wall, minimizing the difference between φf and φp. Numerical simulation of the model with specific parameter values demonstrates that the bat can successfully fly in the chamber while emitting pulses along the inner periphery of an eight-shaped flight path, which is consistent with the results of a behavioral experiment conducted by using a Japanese house bat (Pipistrellus abramus).