A Hodgkin

A Venaille

MI Rabinovich

Mohamad Ghadami

Ramin Azodi

English

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Dynamical behavior of neural ensembles: bifurcation analysis approach

Azodi Ramin

Ghadami Mohamad

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BMC Neuroscience

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POSTER PRESENTATION Open Access
Dynamical behavior of neural ensembles:
bifurcation analysis approach
Ramin Azodi*, Mohamad Ghadami
From Twentieth Annual Computational Neuroscience Meeting: CNS*2011
Stockholm, Sweden. 23-28 July 2011
Computational analysis of neural networks has a signif-
icant effect to recognise the behaviour of synaptic neu-
rons. In the past few years, dynamical systems and
nonlinear phenomena related to dynamics of neurons
achieve much attention. These structures are typically
modeled by set of ordinary differential equations
(ODE) which represent a well understanding approach
in order to explore dynamic behavior of the network
[1]. In fact, these equations are mathematically consis-
tent with the performance of biological structures. One
of the parameters which possesses prominent effect on
the whole activity of the ensembles is the strength
among neural networks that appears in ODE equa-
tions. Changing in strength of a typical network might
lead to transition between phases which are identified
by different local and global bifurcations. In addition,
the main aspect which leads to complexity of these
structures is interactions between intrinsically oscilla-
tory neurons and their influence on each other [2].
These interactions could be considered as coupled sys-
tems among neurons or network oscillators. In coupled
systems each oscillator is determined by a coupling
strength and the states of oscillatory networks. There-
fore, bifurcation analysis can be useful method to be
taken into account.
In this work, we applied bifurcation theory as a pro-
mising mathematical method to reveal the dynamical
behavior of a biological system (neural network zoom
for this purpose). For this purpose the computational of
local and global bifurcations has been done using
AUTO software’s package [3]. Knowing that Saddle
Node bifurcation (SNB) is used to detect stability of the
networks, whereas creations of periodic solutions are
corresponds to Hopf bifurcation (HB). Also, it should be
noted that heteroclinic bifurcation is utilized to investi-
gate sequential switching activity in the neural ensem-
bles in phase space [4]. All of these approaches
employed in analyzing our models. Moreover, the
* Correspondence: ramin.azodi@ut.ac.ir
Department of Mechatronics, University of Tehran-Kish International Campus,
Kish Island, 79416-55665, Iran
Full list of author information is available at the end of the article
Figure 1 A. Phase space diagram of each ensembles. B. Schematic diagram of ensemble. C. The bifurcation diagram of two typical electrical
coupling.
Azodi and Ghadami BMC Neuroscience 2011, 12(Suppl 1):P6
http://www.biomedcentral.com/1471-2202/12/S1/P6
© 2011 Azodi and Ghadami; licensee BioMed Central Ltd. This is an open access article distributed under the terms of the Creative
Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and
reproduction in any medium, provided the original work is properly cited.
synchronous activity of neural populations could be
extracted from ODE equations.
Through the simulation of a single ensemble, we con-
cluded that, increase in number of neurons and conse-
quently connections between them in ensembles leads
to more complexity in dynamical behavior of the system
(Figure 1A). We also found that if we consider some
specific neurons with dominant coupling strength in
comparison with oscillatory neurons in the whole sys-
tems, the ensembles will experience instability in some
cases. Furthermore, in this research electrical coupling
between ensembles had considerable importance for us.
Drawing bifurcation diagram for different kinds of
ensembles let us to deduced that, when the values of
electrical couplings becomes near to each other (Figures
1B and 1C), It shows the chaotic behavior of the system.
We also got some interesting result about the effect of
strength intensity on intrinsically oscillatory neurons.
Further researches on this subject are in progress.
Published: 18 July 2011
References
1. Hodgkin A, Huxley A: A quantitative description of membrane current
and its application to conduction and excitation in nerve. J. Physiol 1952,
117:500-544.
2. Venaille A, Varona P, Rabinovich MI: Synchronization and coordination of
sequences in two neural ensembles. Phys Rev E 2005, 71:1-8.
3. AUTO 07p: Continuation and Bifurcation Software for Ordinary
Differential Equations (with HomCont). [http://sourceforge.net/projects/
auto-07p/].
4. Rabinovich MI, Huerta R, Afraimovich V: Dynamics of sequential decision
making. Phys Rev E 2006, 97:1-8, 97.2006.
doi:10.1186/1471-2202-12-S1-P6
Cite this article as: Azodi and Ghadami: Dynamical behavior of neural
ensembles: bifurcation analysis approach. BMC Neuroscience 2011 12
(Suppl 1):P6.
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Azodi and Ghadami BMC Neuroscience 2011, 12(Suppl 1):P6
http://www.biomedcentral.com/1471-2202/12/S1/P6
Page 2 of 2


A: A quantitative description of membrane current and its application to conduction and excitation in nerve.

Afraimovich V: Dynamics of sequential decision making. Phys Rev E

Submit your next manuscript to BioMed Central and take full advantage of: • Convenient online submission • Thorough peer review • No space constraints or color ﬁgure charges • Immediate publication on acceptance

Synchronization and coordination of sequences in two neural ensembles. Phys Rev E

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Dynamical behavior of neural ensembles: bifurcation analysis approach

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