Citation Relationships



Heitmann S, Breakspear M (2018) Chapter 1 Handbook for the Brain Dynamics Toolbox: Version 2018a :1-88

   Brain Dynamics Toolbox (Heitmann & Breakspear 2016, 2017, 2018)

References and models cited by this paper

References and models that cite this paper

Aburn MJ (2017) Critical fluctuations and coupling of stochastic neural mass models. Ph.D. thesis, University of Queensland

Bower JM, Beeman D (1998) The Book Of Genesis: Exploring Realistic Neural Models With The General Neural Simulation System

Breakspear M, Heitmann S, Daffertshofer A (2010) Generative models of cortical oscillations: neurobiological implications of the kuramoto model. Front Hum Neurosci 4:190 [Journal] [PubMed]

Breakspear M, Terry JR (2002) Detection and description of non-linear interdependence in normal multichannel human EEG data. Clin Neurophysiol 113:735-53 [PubMed]

Breakspear M, Terry JR, Friston KJ (2003) Modulation of excitatory synaptic coupling facilitates synchronization and complex dynamics in a biophysical model of neuronal dynamics. Network 14:703-32 [Journal] [PubMed]

Carnevale NT, Hines ML (2006) The NEURON Book [Journal]

Clewley R (2012) Hybrid models and biological model reduction with PyDSTool. PLoS Comput Biol 8:e1002628 [Journal] [PubMed]

Dafilis MP,Frascoli F,Cadusch PJ,Liley DT (2009) Chaos and generalised multistability in a mesoscopic model of the electroencephalogram Physica D: Nonlinear Phenomena 238(13):1056-1060 [Journal]

Dankowicz H,Schilder F (2013) Recipes for Continuation SIAM. ISBN 978-1- 61197-256-6

Dhooge A, Govaerts W, Kuznetsov YA (2003) MATCONT: A MATLAB package for numerical bifurcation analysis of ODEs Acm Trans Math Softw 29:141-164

Doedel EJ,Champneys AR,Fairgrieve TF,Kuznetsov YA,Sandstede B,Wang X (1997) AUTO 97: Continuation and Bifurcation Software for Ordinary Differential Equations (with HomCont) Montreal, Canada: Concordia University, (Technical Report)

Ermentrout GB (2002) Simulating, Analyzing, and Animating Dynamical System: A Guide to XPPAUT for Researchers and Students Society for Industrial and Applied Mathematics (SIAM)

Fitzhugh R (1955) Mathematical models of threshold phenomena in the nerve membrane Bullmath Biophys 17:257-278

Freyer F, Roberts JA, Ritter P, Breakspear M (2012) A canonical model of multistability and scale-invariance in biological systems. PLoS Comput Biol 8:e1002634 [Journal] [PubMed]

Gardiner C (2009) Stochastic methods: a handbook for the natural and social sciences (Springer series in synergetics)

Goodman DFM, Brette R (2013) Brian simulator Scholarpedia 8(1):10883 [Journal]

Heitmann S, Ermentrout GB (2015) Synchrony, waves and ripple in spatially coupled Kuramoto oscillators with Mexican hat connectivity. Biol Cybern 109:333-47 [Journal] [PubMed]

Heitmann S,Aburn MJ,Breakspear M (2017) The Brain Dynamics Toolbox for Matlab arXiv [Journal]

   Brain Dynamics Toolbox (Heitmann & Breakspear 2016, 2017, 2018) [Model]

Heitmann S,Breakspear M (2017) Putting the "dynamic" back into dynamic functional connectivity bioRxiv [Journal]

Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B Biol Sci 221:87-102 [Journal] [PubMed]

   A model of neuronal bursting using three coupled first order diff. eqs. (Hindmarsh & Rose 1984) [Model]

HODGKIN AL, HUXLEY AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117:500-44 [Journal] [PubMed]

   Squid axon (Hodgkin, Huxley 1952) (LabAXON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (NEURON) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SNNAP) [Model]
   Squid axon (Hodgkin, Huxley 1952) used in (Chen et al 2010) (R language) [Model]
   Squid axon (Hodgkin, Huxley 1952) (SBML, XPP, other) [Model]

Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci U S A 79:2554-8 [PubMed]

Jacobs K (2010) Stochastic processes for physicists: understanding noisy systems

Kloeden PE, Platen E (1992) Numerical Solution Of Stochastic Differential Equations

K├Âtter R (2004) Online retrieval, processing, and visualization of primate connectivity data from the CoCoMac database. Neuroinformatics 2:127-44 [Journal] [PubMed]

Kottwitz S (2011) Latex Beginner's Guide Packt Publishing Ltd

Kuramoto Y (1984) Chemical oscillations, waves, and turbulence

Lamport L (1994) LaTeX: A Document Preparation System, 2nd Edition ISBN 978-0-201-52983-8

Marple L (1999) Computing the discrete-time analytic signal via FFT IEEE Transactions on Signal Processing 47(9):2600-2603 [Journal]

Maruyama G (1955) Continuous Markov processes and stochastic equations Rendiconti del Circolo Matematico di Palermo 4(1):48-90

Park Y,Heitmann S,Ermentrout B (2017) The utility of phase models in studying neuronal synchronization Computational models of brain and behavior, 1st edn :493-504

Rand RH, Holmes PJ (1980) Bifurcations of periodic motions in two weakly coupled van der Pol oscillators Int J Nonlinear Mec 15:387-399

Roberts JA, Friston KJ, Breakspear M (2017) Clinical Applications of Stochastic Dynamic Models of the Brain, Part I: A Primer. Biol Psychiatry Cogn Neurosci Neuroimaging 2:216-224 [Journal] [PubMed]

Rubinov M, Sporns O (2010) Complex network measures of brain connectivity: uses and interpretations. Neuroimage 52:1059-69 [Journal] [PubMed]

Ruemelin W (1982) Numerical treatment of stochastic differential equations SIAM Journal on Numerical Analysis 19(3):604-613

Sanz Leon P, Knock SA, Woodman MM, Domide L, Mersmann J, McIntosh AR, Jirsa V (2013) The Virtual Brain: a simulator of primate brain network dynamics. Front Neuroinform 7:10 [Journal] [PubMed]

Sanz-Leon P, Knock SA, Spiegler A, Jirsa VK (2015) Mathematical framework for large-scale brain network modeling in The Virtual Brain. Neuroimage 111:385-430 [Journal] [PubMed]

Shampine LF,Gladwell I,Thompson S (2003) Solving ODEs with Matlab

Smythe J,Moss F,McClintock PV,Clarkson D (1983) Ito versus Stratonovich revisited Physics Letters A 97(3):95-98

The Mathworks (2017) MATLAB & Simulink: Text with mathematical expression using LaTeX

Van der Pol B (1934) The nonlinear theory of electric oscillations Proceedings of the Institute of Radio Engineers 22(9):1051-1086

van_Kampen NG (1981) Ito versus Stratonovich J Stat Phys 24:175-187

Van_kampen NG (1992) Stochastic Processes In Physics And Chemistry

Wille DR,Baker CT (1992) DELSOL - a numerical code for the solution of systems of delay-differential equations Applied Numerical Mathematics 9(3-5):223-234

(44 refs)