We present Conedy, a performant scientific tool to numerically investigate dynamics on complex networks. Conedy allows to create networks and provides automatic code generation and compilation to ensure performant treatment of arbitrary node dynamics. Conedy can be interfaced via an internal script interpreter or via a Python module.

1.
S.
Boccaletti
,
V.
Latora
,
Y.
Moreno
,
M.
Chavez
, and
D.-U.
Hwang
,
Phys. Rep.
424
,
175
(
2006
).
2.
A.
Barrat
,
M.
Barthélemy
, and
A.
Vespignani
,
Dynamical Processes on Complex Networks
(
Cambridge University Press
,
New York, USA
,
2008
).
3.
E.
Bullmore
and
O.
Sporns
,
Nat. Rev. Neurosci.
10
,
186
(
2009
).
4.
D. J.
Watts
and
S. H.
Strogatz
,
Nature (London)
393
,
440
(
1998
).
5.
A.-L.
Barabási
and
R.
Albert
,
Science
286
,
509
(
1999
).
6.
M. E. J.
Newman
,
S. H.
Strogatz
, and
D. J.
Watts
,
Phys. Rev. E
64
,
026118
(
2001
).
7.
G.
Caldarelli
,
A.
Capocci
,
P.
De Los Rios
, and
M. A.
Muñoz
,
Phys. Rev. Lett.
89
,
258702
(
2002
).
8.
M.
Catanzaro
,
M.
Boguñá
, and
R.
Pastor-Satorras
,
Phys. Rev. E
71
,
027103
(
2005
).
9.
R.
Pastor-Satorras
and
A.
Vespignani
,
Phys. Rev. Lett.
86
,
3200
(
2001
).
10.
T.
Zhou
,
Z.
Fu
, and
B.
Wang
,
Prog. Nat. Sci.
16
,
452
(
2006
).
11.
T. E.
Stone
and
S. R.
McKay
,
Europhys. Lett.
95
,
38003
(
2011
).
12.
T. I.
Netoff
,
R.
Clewley
,
S.
Arno
,
T.
Keck
, and
J. A.
White
,
J. Neurosci.
24
,
8075
(
2004
).
13.
B.
Percha
,
R.
Dzakpasu
,
M.
Zochowski
, and
J.
Parent
,
Phys. Rev. E
72
,
031909
(
2005
).
14.
J.
Dyhrfjeld-Johnsen
,
V.
Santhakumar
,
R. J.
Morgan
,
R.
Huerta
,
L.
Tsimring
, and
I.
Soltesz
,
J. Neurophysiol.
97
,
1566
(
2007
).
15.
S.
Feldt
,
H.
Osterhage
,
F.
Mormann
,
K.
Lehnertz
, and
M.
Zochowski
,
Phys. Rev. E
76
,
021920
(
2007
).
16.
R. J.
Morgan
and
I.
Soltesz
,
Proc. Natl. Acad. Sci. U.S.A.
105
,
6179
(
2008
).
17.
A.
Rothkegel
and
K.
Lehnertz
,
Chaos
19
,
015109
(
2009
).
18.
P.
Stratton
and
J.
Wiles
,
NeuroImage
52
,
1070
(
2010
).
19.
O.
Kwon
,
H.-H.
Jo
, and
H.-T.
Moon
,
Phys. Rev. E
72
,
066121
(
2005
).
20.
W.
Mao-Sheng
,
H.
Zhong-Huai
, and
X.
Hou-Wen
,
Chin. Phys.
15
,
2553
(
2006
).
21.
J.
Ren
,
W.
Wang
,
B.
Li
, and
Y.-C.
Lai
,
Phys. Rev. Lett.
104
,
058701
(
2010
).
22.
C. W.
Wu
,
Synchronization in Complex Networks of Nonlinear Dynamical Systems
(
World Scientific
,
Singapore
,
2007
).
23.
A.
Arenas
,
A.
Díaz-Guilera
,
J.
Kurths
,
Y.
Moreno
, and
C.
Zhou
,
Phys. Rep.
469
,
93
(
2008
).
24.
J. A. K.
Suykens
and
G. V.
Osipov
,
Chaos
18
,
037101
(
2008
).
25.
K.
Lehnertz
,
S.
Bialonski
,
M.-T.
Horstmann
,
D.
Krug
,
A.
Rothkegel
,
M.
Staniek
, and
T.
Wagner
,
J. Neurosci. Methods
183
,
42
(
2009
).
26.
J. A.
Almendral
,
R.
Criado
,
I.
Leyva
,
J. M.
Buldú
, and
I.
Sendiña-Nadal
,
Chaos
21
,
016101
(
2011
).
27.
28.
R.
Albert
and
A.-L.
Barabási
,
Rev. Mod. Phys.
74
,
47
(
2002
).
29.
M. E. J.
Newman
,
SIAM Rev.
45
,
167
(
2003
).
30.
L. da F.
Costa
,
F. A.
Rodrigues
,
G.
Travieso
, and
P. R. V.
Boas
,
Adv. Phys.
56
,
167
(
2007
).
31.
H. D. I.
Abarbanel
,
R.
Brown
,
J. J.
Sidorowich
, and
L. S.
Tsimring
,
Rev. Mod. Phys.
65
,
1331
(
1993
).
32.
R.
Hegger
,
H.
Kantz
, and
T.
Schreiber
,
Chaos
9
,
413
(
1999
).
33.
H.
Kantz
and
T.
Schreiber
,
Nonlinear Time Series Analysis
, 2nd ed. (
Cambridge University Press
,
Cambridge, UK
,
2003
).
34.
A. S.
Pikovsky
,
M. G.
Rosenblum
, and
J.
Kurths
,
Synchronization: A Universal Concept in Nonlinear Sciences
(
Cambridge University Press
,
Cambridge, UK
,
2001
).
35.
E.
Pereda
,
R. Q.
Quiroga
, and
J.
Bhattacharya
,
Prog. Neurobiol.
77
,
1
(
2005
).
36.
K.
Hlaváčková-Schindler
,
M.
Paluš
,
M.
Vejmelka
, and
J.
Bhattacharya
,
Phys. Rep.
441
,
1
(
2007
).
37.
R. V.
Donner
,
Y.
Zou
,
J. F.
Donges
,
N.
Marwan
, and
J.
Kurths
,
New J. Phys.
12
,
033025
(
2010
).
38.
H. E.
Nusse
and
J. A.
Yorke
,
Dynamics: Numerical Explorations
(
Springer
,
New York, Berlin
,
1998
).
39.
B.
Ermentrout
,
Simulating, Analyzing, and Animating Dynamical Systems: A Guide to XPPAUT for Researchers and Students
(
SIAM
,
Philadelphia, PA
,
2002
).
40.
A.
Dhooge
,
W.
Govaerts
, and
Y. A.
Kuznetsov
,
ACM Trans. Math. Softw.
29
,
141
(
2003
).
41.
R. H.
Clewley
,
W. E.
Sherwood
,
M. D.
LaMar
, and
J. M.
Guckenheimer
,
“Pydstool, a software environment for dynamical systems modeling,”
http://pydstool.sourceforge.net.
42.
J. M.
Bower
and
D.
Beeman
,
The Book of GENESIS: Exploring Realistic Neural Models with the General Neural Simulation System
(
Springer
,
Berlin
,
1998
).
43.
N. T.
Carnevale
and
M. L.
Hines
,
The Neuron Book
(
Cambridge University Press
,
Cambridge, UK
,
2006
).
44.
M.-O.
Gewaltig
and
M.
Diesmann
,
“NEST (NEural Simulation Tool)
Scholarpedia
2
,
1430
(
2007
).
45.
D.
Goodman
and
R.
Brette
,
Front. Neuroinform.
2
,
5
(
2008
).
46.
M.
Hines
,
A. P.
Davison
, and
E.
Muller
,
Front. Neuroinform.
3
,
1
(
2009
).
47.
D.
Pecevski
,
T.
Natschläger
, and
K.
Schuch
,
Front. Neuroinform.
3
,
11
(
2009
).
48.
T. E.
Oliphant
,
Comput. Sci. Eng.
9
,
10
(
2007
).
49.
G. V.
Osipov
,
B.
Hu
,
C.
Zhou
,
M. V.
Ivanchenko
, and
J.
Kurths
,
Phys. Rev. Lett.
91
,
024101
(
2003
).
50.
J.
Nawrath
,
M. C.
Romano
,
M.
Thiel
,
I. Z.
Kiss
,
M.
Wickramasinghe
,
J.
Timmer
,
J.
Kurths
, and
B.
Schelter
,
Phys. Rev. Lett.
104
,
038701
(
2010
).
51.
M.
Galassi
,
J.
Davies
,
J.
Theiler
,
B.
Gough
,
G.
Jungman
,
P.
Alken
,
M.
Booth
, and
F.
Rossi
,
GNU Scientific Library Reference Manual
, 3rd ed. (
Network Theory Ltd.
,
UK
,
2009
).
52.
P. E.
Kloeden
and
E.
Platen
,
Numerical Solution of Stochastic Differential Equations
(
Springer
,
Berlin
,
1999
).
53.
R.
Brette
,
M.
Rudolph
,
T.
Carnevale
,
M.
Hines
,
D.
Beeman
,
J.
Bower
,
M.
Diesmann
,
A.
Morrison
,
P.
Goodman
,
F.
Harris
,
M.
Zirpe
,
T.
Natschläger
,
D.
Pecevski
,
B.
Ermentrout
,
M.
Djurfeldt
,
A.
Lansner
,
O.
Rochel
,
T.
Vieville
,
E.
Muller
,
A.
Davison
,
S.
El Boustani
, and
A.
Destexhe
,
J. Comput. Neurosci.
23
,
349
(
2007
).
54.
J. R.
Driscoll
,
H. N.
Gabow
,
R.
Shrairman
, and
R. E.
Tarjan
,
Commun. ACM
31
,
1343
(
1988
).
55.
56.
R. E.
Mirollo
and
S. H.
Strogatz
,
SIAM J. Appl. Math.
50
,
1645
(
1990
).
57.
Y.
Kuramoto
,
Chemical Oscillations, Waves and Turbulence
(
Springer Verlag
,
Berlin
,
1984
).
58.
K. T.
Alligood
,
T. D.
Sauer
, and
J. A.
Yorke
,
Chaos An Introduction to Dynamical Systems
(
Springer
,
New York
,
1996
).
59.
E. M.
Izhikevich
,
Dynamical Systems in Neuroscience: The Geometry of Excitability and Bursting
(
MIT, Cambridge
,
MA
,
2007
).
62.
G.
Csardi
and
T.
Nepusz
,
InterJournal Complex Syst.
1695
(
2006
).
63.
A. A.
Hagberg
,
D. A.
Schult
, and
P. J.
Swart
,
‘‘Exploring network structure, dynamics, and function using networkx,’’
in
Proceedings of the 7th Python in Science Conference (SciPy2008)
(
Pasadena, CA, USA
,
2008
), pp.
11
15
.
64.
A.
Zumdieck
,
M.
Timme
,
T.
Geisel
, and
F.
Wolf
,
Phys. Rev. Lett.
93
,
244103
(
2004
).
65.
A.
Rothkegel
and
K.
Lehnertz
,
Europhys. Lett.
95
,
38001
(
2011
).
66.
Conedy uses a 32 bit integer as identifier for the target node of the edge. For edges with virtual functions, 64 bit is needed for the jump table and most modern compiler will leave another 32 bit empty due to alignment of the data structures.
67.
S.
Olmi
,
R.
Livi
,
A.
Politi
, and
A.
Torcini
,
Phys. Rev. E
81
,
046119
(
2010
).
68.
S.
Jahnke
,
R.-M.
Memmesheimer
, and
M.
Timme
,
Front. Comput. Neurosci.
3
,
13
(
2009
).
69.
We assume that neurons are described by a membrane potential v(t), which is governed by dv(t)/dt=-av(t)+b, while every presynaptic firing neuron at time tf induces a jump v(tf+)=v(tf)±c.
70.
W. H.
Press
,
S. A.
Teukolsky
,
W. T.
Vetterling
, and
B. P.
Flannery
,
Numerical Recipes: The Art of Scientific Computing,
3rd ed. (
Cambridge University Press
,
Cambridge, UK
,
2007
).
You do not currently have access to this content.