Neural-Based Control of Compliant Foils With Spanwise Flexibility

The ability to change the spatial distribution of a compliant foil’s flexural rigidity can enhance the foil’s swimming performance capabilities but pose challenges to neural-based control of these types of foils. The same property that makes these foil’s effective propulsors also makes them challenging to control with a neural oscillator, namely the variation in the mechanical properties will cause the amplitude and phase of the sensory feedback signal to vary depending upon the placement of the sensor. In this study we investigate the effect of sensor placement on the entrainment characteristics of a coupled-system consisting of a neural oscillator driving a series of compliant foils with spanwise flexibility (i.e. spatially varying mechanical properties in the dorsal-ventral direction). We find that acquiring sensory feedback from the foil’s stiff region produces a broader range of frequencies over which entrainment occurs compared to acquiring feedback from the compliant region of a foil. Additionally, we characterize the thrust and lift forces generated by spanwise foils as a function of the foil’s flapping frequency and flexural rigidity.

Quasiperiodicity and Chaos Through Hopf–Hopf Bifurcation in Minimal Ring Neural Oscillators Due to a Single Shortcut

Quasiperiodicity and chaos in a ring of unidirectionally coupled sigmoidal neurons (a ring neural oscillator) caused by a single shortcut is examined. A codimension-two Hopf–Hopf bifurcation for two periodic solutions exists in a ring of six neurons without self-couplings and in a ring of four neurons with self-couplings in the presence of a shortcut at specific locations. The locus of the Neimark–Sacker bifurcation of the periodic solution emanates from the Hopf–Hopf bifurcation point and a stable quasiperiodic solution is generated. Arnold’s tongues emanate from the locus of the Neimark–Sacker bifurcation, and multiple chaotic oscillations are generated through period-doubling cascades of periodic solutions in the Arnold’s tongues. Further, such chaotic irregular oscillations due to a single shortcut are also observed in propagating oscillations in a ring of Bonhoeffer–van der Pol (BVP) neurons coupled unidirectionally by slow synapses.