Dynamics of Optimal Cue Integration with Time-Varying Delay in the Insects' Navigation System

Neural networks with a ring structure are considered biologically plausible and have the ability of enforcing unique and persistent heading representations, yielding realistic homing behaviors. Recent studies have found that insects optimally integrate sensory information from the environment for head direction by using ring attractor networks. Optimal cue integration as the basic component of a complex insect navigation system proves to consist of a ring attractor network that is coupled by some integration neurons and some uniform inhibition neurons. The dynamics of the coupled mechanisms between neurons in optimal cue integration determine whether the insects' homing capability is affected by environmental noises. Furthermore, time delays caused by communication between different kinds of neurons may induce complex dynamical properties. These dynamical behaviors are essential for understanding the neural mechanisms of insect homing behaviors, but there is a lack of relevant research on the dynamics of optimal cue integration with time-varying delay in the insects' navigation system. In this paper, we discuss the dynamical properties of optimal cue integration with time-varying delay and show that it is asymptotically stable and leads to a unique insect home direction. These results are critical in providing the theoretical basis for further research on insect homing behaviors and the establishment of autonomous robots that mimic insect navigation mechanisms in the future.