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. 2013 Jan 11;8(1):e53854. doi: 10.1371/journal.pone.0053854

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© 2013 Kanamaru et al

This is an open-access article distributed under the terms of the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original author and source are properly credited.

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(A), (B), and (C) Chaotic synchronization observed in a unit model with PYRs and INs. The values of the parameters are , , , , , , , , , and . (A) Raster plot of spikes of 100 PYRs and 25 INs (randomly chosen). The firing times of neurons have correlations and we call such firing synchronized. (B) Temporal changes in instantaneous firing rates and of the excitatory ensemble and the inhibitory ensemble , respectively, calculated from the firing in Figure A. It is observed that and fluctuate, and it is found that this fluctuation is caused by chaotic dynamics and not by a stochastic one. (C) Trajectory in the (, ) plane obtained from the data in Figure B. It is observed that the trajectory has some complex structure. (D) Asynchronous firing observed in this unit. Raster plot of spikes of 100 PYRs and 25 INs (randomly chosen). The number of firing is very few because the firing rates are low. (E) and (F) Chaotic synchronization in a unit with an infinite number of neurons obtained by analysis with Fokker-Planck equations, which corresponds to the results in Figures B and C obtained in a unit with a finite number of neurons. (E) Temporal changes in the instantaneous firing rates and . The results are similar to those in Figure B. (F) Trajectory in the (, ) plane. A fine structure of a chaotic attractor is visible.

Inline graphic — (A), (B), and (C) Chaotic synchronization observed in a unit model with PYRs and INs. The values of the parameters are , , , , , , , , , and . (A) Raster plot of spikes of 100 PYRs and 25 INs (randomly chosen). The firing times of neurons have correlations and we call such firing synchronized. (B) Temporal changes in instantaneous firing rates and of the excitatory ensemble and the inhibitory ensemble , respectively, calculated from the firing in Figure A. It is observed that and fluctuate, and it is found that this fluctuation is caused by chaotic dynamics and not by a stochastic one. (C) Trajectory in the (, ) plane obtained from the data in Figure B. It is observed that the trajectory has some complex structure. (D) Asynchronous firing observed in this unit. Raster plot of spikes of 100 PYRs and 25 INs (randomly chosen). The number of firing is very few because the firing rates are low. (E) and (F) Chaotic synchronization in a unit with an infinite number of neurons obtained by analysis with Fokker-Planck equations, which corresponds to the results in Figures B and C obtained in a unit with a finite number of neurons. (E) Temporal changes in the instantaneous firing rates and . The results are similar to those in Figure B. (F) Trajectory in the (, ) plane. A fine structure of a chaotic attractor is visible.