ENTRAINMENT, INSTABILITY, QUASI-PERIODICITY, AND CHAOS IN A COMPOUND NEURAL OSCILLATOR

We studied the dynamical behavior of a class of compound central patte rn generator (CPG) models consisting of a simple neural network oscill ator driven by both constant and periodic inputs of varying amplitudes , frequencies, and phases. We focused on a specific oscillator compose d of two mutually inhibiting types of neuron (inspiratory and expirato ry neurons) that may be considered as a minimal model of the mammalian respiratory rhythm generator. The simulation results demonstrated how a simple CPG model-with a minimum number of neurons and mild nonlinea rities-may reproduce a host of complex dynamical behaviors under vario us periodic inputs. In particular, the network oscillated spontaneousl y only when both neurons received adequate and proportionate constant excitations. In the presence of a periodic source, the spontaneous rhy thm was overriden by an entrained oscillation of varying forms dependi ng on the nature of the source. Stable entrained oscillations were ind ucible by two types of inputs: (1) anti-phase periodic inputs with alt ernating agonist-antagonist drives to both neurons and (2) a single pe riodic drive to only one of the neurons. In-phase inputs, which exert periodic drives of similar magnitude and phase relationships to both n eurons, resulted in varying disruptions of the entrained oscillations including magnitude attenuation, harmonic and phase distortions, and q uasi-periodic interference. In the absence of significant phasic feedb ack, chaotic motion developed only when the CPG was driven by multiple periodic inputs. Apneic episodes with repetitive alternation of activ e (intrinsic oscillation) and inactive (cessation of oscillation) stat es developed when the network was driven by a moderate periodic input of low frequency. Similar results were demonstrated in other, more com plex oscillator models (that is, half-center oscillator and three-phas e respiratory network model). These theoretical results may have impor tant implications in elucidating the mechanisms of rhythmogenesis in t he mature and developing respiratory CPG as well as other compound CPG s in mammalian and invertebrate nervous systems.