Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns.
Period-doubling bifurcation to chaos were discovered in spontaneous firings of Onchidium pacemaker neurons. In this paper, we provide three cases of bifurcation processes related to period-doubling bifurcation cascades to chaos observed in the spontaneous firing patterns recorded from an injured site of rat sciatic nerve as a pacemaker. Period-doubling bifurcation cascades to period-4 (π(2,2)) firstly, and then to chaos, at last to a periodicity, which can be period-5, period-4 (π(4)) and period-3, respectively, in different pacemakers. The three bifurcation processes are labeled as case I, II and III, respectively, manifesting procedures different to those of period-adding bifurcation. Higher-dimensional unstable periodic orbits (UPOs) can be detected in the chaos, built close relationships to the periodic firing patterns. Case III bifurcation process is similar to that discovered in the Onchidium pacemaker neurons and simulated in theoretical model-Chay model. The extra-large Feigenbaum constant manifesting in the period-doubling bifurcation process, induced by quasi-discontinuous characteristics exhibited in the first return maps of both ISI series and slow variable of Chay model, shows that higher-dimensional periodic behaviors appeared difficult within the period-doubling bifurcation cascades. The results not only provide examples of period-doubling bifurcation to chaos and chaos with higher-dimensional UPOs, but also reveal the dynamical features of the period-doubling bifurcation cascades to chaos.
School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092 China  ; College of Life Science, Shaanxi Normal University, Xi'an, 710062 Shaanxi China.
Bing
B
Jia
Huaguang
H
Gu
Li
L
Li
Xiaoyan
X
Zhao
Chaos; Feigenbaum constant; Neural firing pattern; Non-smooth characteristic; Period-adding bifurcation; Period-doubling bifurcation; Quasi-discontinuous characteristic; Unstable periodic orbits