Exact digital simulation of time-invariant linear systems with applications to neuronal modeling

Biological Cybernetics

Volumn 81, Issue 5-6, 1999, Pages 381-402

  Rotter, Stefan ^a   Diesmann, Markus ^a  

^a UNIVERSITY OF FREIBURG   (Germany)

Author keywords

[No Author keywords available]

Indexed keywords

ANIMAL; ARTICLE; BIOLOGICAL MODEL; COMPUTER SIMULATION; CYBERNETICS; EVOKED RESPONSE; HUMAN; NERVE CELL; NERVE CELL NETWORK; PHYSIOLOGY; STATISTICAL MODEL; TIME;

ANIMALS; COMPUTER SIMULATION; CYBERNETICS; EVOKED POTENTIALS; HUMANS; LINEAR MODELS; MODELS, NEUROLOGICAL; NERVE NET; NEURONS; TIME FACTORS;

EID: 0033220632     PISSN: 03401200     EISSN: None     Source Type: Journal    
DOI: 10.1007/s004220050570     Document Type: Article

References (38)

1. Arnol'd VI (1992) Ordinary differential equations, 3rd edn. Springer, Berlin Heidelberg New York
2. Bernard C, Ge YC, Stockley E, Willis JB, Wheal HV (1994) Synaptic integration of NMDA and non-NMDA receptors in large neuronal network models solved by means of differential equations. Biol Cybern 70:267-273
3. Bower JM, Beeman D (1997) The book of GENESIS: Exploring realistic neural models with the GEneral NEural Simulation System, 2nd edn. TELOS, Springer, New York Berlin Heidelberg
4. Bronstein IN, Semendjajew KA, Grosche G, Ziegler V, Ziegler D, Zeidler E (1996) Teubner-Taschenbuch der Mathematik, 25th edn. Teubner, Stuttgart, Leipzig
5. Colquhoun D, Hawkes AG (1977) Relaxation and fluctuations of membrane currents that flow through drug-operated channels. Proc R Soc Lond B 199:231-262
6. Colquhoun D, Hawkes AG (1981) On the stochastic properties of ion channels. Proc R Soc Lond B 211:205-235
7. Colquhoun D, Hawkes AG (1982) On the stochastic properties of bursts of single channel openings and of clusters of bursts. Proc R Soc Lond B 300:1-59
8. Colquhoun D, Hawkes AG (1995a) The principles of the stochastic interpretation of ion-channel mechanisms. In: Sakmann B, Neher E (eds) Single-channel recording, chap 18, 2nd edn. Plenum Press, New York, pp 397-482
9. Colquhoun D, Hawkes AG (1995b) A Q-matrix cookbook: how to write only one program to calculate the single-channel and macroscopic predictions for any kinetic mechanism. In: Sakmann B, Neher E (eds) Single-channel recording, chap 20, 2nd edn. Plenum Press, New York, pp 397-482
10. Druskin V, Greenbaum A, Knizhnerman L (1998) Using nonorthogonal Lanczos vectors in the computation of matrix functions. SIAM J Appl Math 19:38-54
11. Golub GH, van Loan CF (1996) Matrix computations, 3rd edn. Johns Hopkins University Press, Baltimore
12. Hansel D, Mato G, Meunier C, Neltner L (1998) On numerical simulations of integrate-and-fire neural networks. Neural Comp 10:467-483
13. Heal KM, Hansen M, Rickard K (1997) Maple V learning guide for release 5. Springer, Berlin Heidelberg New York
14. Hines M, Carnival NT (1995) Computer modeling for neurons. In: Arbib MA (ed) The handbook of brain theory and neural networks. MIT Press, Cambridge, Mass, pp 226-230
15. Hines M, Carnevale NT (1997) The NEURON simulation environment. Neural Comp 9:1179-1209
16. Hirsch M, Smale S (1974) Differential equations, dynamical systems, and linear algebra. Academic Press, San Diego
17. Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol (Lond) 117:500-544
18. Jack JJB, Noble D, Tsien RW (1983) Electric current flow in excitable cells. Oxford University Press, Oxford
19. Kenny CS, Laub AJ (1998) A Schur-Fréchet a logrithm for computing the logarithm and exponential of a matrix. SIAM J Matrix Anal Appl 19:640-663
20. Knight BW (1972) Dynamics of encoding in a population of neurons. J Gen Physiol 59:734-766
21. Leonard IE (1996) The matrix exponential. SIAM Rev 38:507-512
22. MacGregor RJ (1987) Neural and brain modeling. Academic Press. San Diego
23. Mascagni MV (1989) Numerical methods for neuronal modeling. In: Koch C, Segev I (eds) Methods in neuronal modeling: from synapses to networks, chap 13. A Bradford book. MIT Press, Cambridge, Mass, pp 439-440
24. MathWorks Inc. (1998) MATLAB the language of technical computing: using MATLAB. Natick, Mass
25. Moler C, von Loan C (1978) Nineteen dubious ways to compute the exponent of a matrix. SIAM Rev 20:801-836
26. Papoulis A (1991) Probability, random variables, and stochastic processes, 3rd edn. McGraw-Hill, New York
27. Press WH, Teukolsky SA, Vetterling WT, Flannery BP (1992) Numerical recipes in C, 2nd edn. Cambridge University Press, Cambridge
28. Rall W (1964) Theoretical significance of dendritic trees for neuronal input-output relations. In: Reiss RF (ed) Neural theory and modeling. Stanford University Press, Palo Alto
29. Rudin W (1991) Functional analysis, 2nd edn. WBC/McGraw-Hill, New York
30. Scheja G, Storch U (1980) Lehrbuch der Algebra. Teubner, Stuttgart
31. Stein RB (1965) A theoretical analysis of neuronal variability. Biophys 15:173-194
32. Stoer J, Bulirsch R (1996) Introduction to numerical analysis, 2nd edn. Springer, Berlin Heidelberg New York
33. Troyer TW, Miller KD (1997) Physiological gain leads to high ISI variability in a simple model of a cortical regular spiking cell. Neural Comp 9:971-983
34. Tuckwell HC (1988) Introduction to theoretical neurobiology, vol 1. Cambridge University Press, Cambridge
35. Vreeswijk C van, Sompolinsky H (1996) Chaos in neuronal networks with balanced excitatory and inhibitory activity. Science 274:1724-1726
36. Walter W (1996) Gewöhnliche Differentialgleichungen: eine Einführung, 6th edn. Springer, Berlin Heidelberg New York
37. Wilson MA, Bower JM (1989) The simulation of large-scale neural networks. In: Koch C, Segev I (eds) Methods in neuronal modeling: from synapses to networks, chap 9. A Bradford book. MIT Press, Cambridge Mass, pp 291-333
38. Wolfram S (1996) The Mathematica book, 3rd edn. Wolfram Media/Cambridge University Press, Cambridge