Transition to Burst Synchronization on Complex Neuron Networks

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Transition to Burst Synchronization onComplex
Neuron Networks

• Zhonghuai Hou(???)
• 2007.9 Nanjing
• Department of Chemical Physics
• Hefei National Lab of Physical Science at
  Microscale
• University of Science and Technology of China

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Our research interest

• Statistical problems in mesoscopic chemical
  systems

Complexity Nonlinearity

• Nonlinear Dynamics on complex networks

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A Neuron
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Diversity Morphology Physiology

• Oscillation
• Spiking
• Bursting
• Chaos

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Neuron Network

• Human Brain 1011 and 104

Complex Network
Small-World Scale-Free

• Big Challenge Dynamics Functioning

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An interesting phenomenon ...

• Central Pattern Generator
• Small microcircuits
• Rhythmic motor commands
• Striking feature
• Individual irregular,chaotic bursts
• Ensemble regular, rhythmic bursting

Mechanism ?
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Related study

• Chaos Regularization

N.F.Rulkov, PRL 86,183(2001)
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Related study

• Ordering Chaos by Random Shortcuts

F. Qi, Z.Hou, H. Xin, PRL 91, 064102 (2003)
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Related Study

• Ordering Bursting Chaos

Hindmarsh-Rose (HR) model system
M. Wang, Z.Hou, H.Xin. ChemPhysChem 7,579( 2006)
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Synchronization of Bursting System

• Beyond complete synchronization

Spike Syn...
Burst Syn...
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The present work

• Fixed Network increased coupling
• Transition from chaos to BS
• Different types of BS-states
• Spike-adding
• Bursting bifurcation
• Dynamic cluster separation
• Homoclinic orbits shrinking
• Local mean field analysis

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The model

• Coupled HR system

SW Network N neurons M added links
Parameters
Chaotic
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Transition to BS
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Phase Trajectories
Bursting Bifur...
Spike Adding
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Phase Transitions
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Bursting Mechanism
Homoclinic Shrinking
Fast sub-system
Slow Parameter
Fold-Homoclinic(FHC)
Fold-Hopf(FH)
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Local Mean Field

• Fluctuate
• Close to 0
• Depend weakly on i

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Perturbed HR system
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Cluster separation
Valid Robust
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Remarks
Easier
5 SPB
(Homogeneous)
Hard
6 SPB
Easy
FH
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Conclusion

• Transition to BS is investigated
• Two distinct types of transition
• Neuron degree is important
• Local mean field approximation
• Large, Homogeneous HR network with many random
  links in between can show transition from
  spatiotemporal chaos to
• BS-states with FHC- and FH-bursting

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• Thank you !