Dynamics of period-doubling bifurcation to chaos in the spontaneous neural firing patterns |
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Authors: | Bing Jia Huaguang Gu Li Li and Xiaoyan Zhao |
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Institution: | (1) School of Aerospace Engineering and Applied Mechanics, Tongji University, Shanghai, 200092, China;(2) College of Life Science, Shaanxi Normal University, Xi’an, 710062, Shaanxi, China;(3) Science and Training Center of Chinese Astronautics, Beijing, 100193, China; |
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Abstract: | 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. |
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Keywords: | |
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