Bifurcation Scenarios of Neural Firing Patterns across Two Separated Chaotic Regions as Indicated by Theoretical and Biological Experimental Models

Huaguang Gu,Jian Xu,Baobao Pan

doi:10.1155/2013/374674

Abstract

Nonlinear dynamics can be used to identify relationships between different firing patterns, which play important roles in the information processing. The present study provides novel biological experimental findings regarding complex bifurcation scenarios from period-1 bursting to period-1 spiking with chaotic firing patterns. These bifurcations were found to be similar to those simulated using the Hindmarsh-Rose model across two separated chaotic regions. One chaotic region lay between period-1 and period-2 burstings. This region has not attracted much attention. The other region is a well-known comb-shaped chaotic region, and it appears after period-2 bursting. After period-2 bursting, the chaotic firings lay in a period-adding bifurcation scenario or in a period-doubling bifurcation cascade. The deterministic dynamics of the chaotic firing patterns were identified using a nonlinear prediction method. These results provided details regarding the processes and dynamics of bifurcation containing the chaotic bursting between period-1 and period-2 burstings and other chaotic firing patterns within the comb-shaped chaotic region. They also provided details regarding the relationships between different firing patterns in parameter space.

Highlights

Nonlinear dynamics have been instrumental in the improvement of human understanding of the dynamics of neural firing patterns, which have been shown to play important roles in information processing [1,2,3]
Bifurcation processes from period-1 bursting to period-1 spiking with chaotic bursting between period-1 bursting and period-1 spiking and chaotic firing patterns within the comb-shaped chaotic region were observed in 5 out of these 23 pacemakers
The present study focused on the 5 bifurcation processes from period-1 bursting to period-1 spiking with chaotic bursting between period-1 bursting and period-1 spiking and chaotic firing patterns

Summary

Introduction

Nonlinear dynamics have been instrumental in the improvement of human understanding of the dynamics of neural firing patterns, which have been shown to play important roles in information processing [1,2,3]. The complex bifurcation scenario from period-1 bursting to period-1 spiking was simulated as parameter r decreased or I increased across the comb-shaped chaotic region [11,12,13, 22]. Bifurcation scenarios from period-1 bursting to period-1 spiking across the two separated chaotic regions, like the behaviors along lines L1, L2, and L3, are not simulated in the HR model or observed in biological experiments. In previous biological experiments, which were performed on neural pacemakers, the bifurcation scenarios from period-1 bursting to period-1 spiking with chaotic firings, which locate within the comb-shaped chaotic region, were observed [32, 33].

Simulation Results in the HR Model

Experimental Model

Experimental Results

Conclusion and Discussion

Chaotic bursting 2