Heterogeneous Inputs to Central Pattern Generators Can Shape Insect Gaits

In our previous work [SIAM J. Appl. Dyn. Syst., 17 (2018), pp. 626{671], we studied an interconnected bursting neuron model for insect locomotion, and its corresponding phase oscillator model, which at high speed can generate stable tripod gaits with three legs off the ground simultaneously in swing and at low speed can generate stable tetrapod gaits with two legs off the ground simultaneously in swing. However, at low speed several other stable locomotion patterns that are not typically observed as insect gaits may coexist. In the present paper, by adding heterogeneous external input to each oscillator, we modify the bursting neuron model so that its corresponding phase oscillator system produces only one stable gait at each speed, specifically a unique stable tetrapod gait at low speed, a unique stable tripod gait at high speed, and a unique branch of stable transition gaits connecting them. This suggests that control signals originating in the brain and central nervous system can modify gait patterns.