Self-/mutual-symmetric rhythms and their coexistence in a delayed half-center oscillator of the CPG neural system.

Most animals are capable of efficient locomotion owing to a special neural network—the central pattern generator (CPG) located in the central nervous system. The half-center oscillator (HCO) is the basic and pivotal motif of the CPG, which consists of two neurons or two neural populations connected by excitatory and inhibitory neurotransmitters. In this study, we present a simple delayed HCO neural system consisting of two inertial neurons and study the rhythm activities of the system and their coexistence. The periodic orbit, quasi-periodic activity, and chaotic attractor with self- and mutual-symmetric patterns are investigated through their time history, phase diagram, frequency spectra, and Poincaré maps. The one-dimensional bifurcation diagram presents different routes to chaos. A pair of mutual-symmetric periodic orbits surrounding nontrivial equilibria enters a pair of mutual-symmetric chaotic attractors by the period-doubling bifurcation. A self-symmetric periodic orbit evolves into a self-symmetric chaotic attractor by the quasi-periodic bifurcation. Finally, the chaotic attractor translates into a pair of mutual-symmetric multi-periodic orbits and enters a pair of mutual-symmetric chaotic attractors by the period-doubling bifurcation. The HCO neural system illustrates multiple coexistences, such as self-symmetric quasi-periodic orbit with a pair of mutual-symmetric chaotic attractors, a pair of multi-period orbits with chaotic attractors, and two pairs of mutual-symmetric chaotic attractors. [ABSTRACT FROM AUTHOR]