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2012 | OriginalPaper | Chapter

Modeling Biological Neural Networks

Authors : Joaquin J. Torres, Pablo Varona

Published in: Handbook of Natural Computing

Publisher: Springer Berlin Heidelberg

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Abstract

In recent years, many new experimental studies on emerging phenomena in neural systems have been reported. The high efficiency of living neural systems to encode, process, and learn information has stimulated an increased interest among theoreticians in developing mathematical approaches and tools to model biological neural networks. In this chapter we review some of the most popular models of neurons and neural networks that help us understand how living systems perform information processing. Beyond the fundamental goal of understanding the function of the nervous system, the lessons learned from these models can also be used to build bio-inspired paradigms of artificial intelligence and robotics.

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Literature
go back to reference Abarbanel HDI, Huerta R, Rabinovich MI, Rulkov NF, Rowat P, Selverston AI (1996) Synchronized action of synaptically coupled chaotic model neurons. Neural Comp 8(8):1567–1602CrossRef Abarbanel HDI, Huerta R, Rabinovich MI, Rulkov NF, Rowat P, Selverston AI (1996) Synchronized action of synaptically coupled chaotic model neurons. Neural Comp 8(8):1567–1602CrossRef
go back to reference Abbott LF, Valera JA, Sen K, Nelson SB (1997) Synaptic depression and cortical gain control. Science 275(5297):220–224CrossRef Abbott LF, Valera JA, Sen K, Nelson SB (1997) Synaptic depression and cortical gain control. Science 275(5297):220–224CrossRef
go back to reference Amari S (1972) Characteristics of random nets of analog neuron-like elements. IEEE Trans Syst Man Cybern 2:643–657CrossRefMATH Amari S (1972) Characteristics of random nets of analog neuron-like elements. IEEE Trans Syst Man Cybern 2:643–657CrossRefMATH
go back to reference Amit D, Tsodyks M (1991) Quantitative study of attractor neural networks retrieving at low spike rates: II. low-rate retrieval in symmetric networks. Network: Comput Neural Syst 2:275–294CrossRefMATH Amit D, Tsodyks M (1991) Quantitative study of attractor neural networks retrieving at low spike rates: II. low-rate retrieval in symmetric networks. Network: Comput Neural Syst 2:275–294CrossRefMATH
go back to reference Arshavsky YI, Beloozerova IN, Orlovsky GN, Panchin YV, Pavlova GA (1985) Control of locomotion in marine mollusc Clione limacina. i. efferent activity during actual and fictitious swimming. Exp Brain Res 58(2):255–293 Arshavsky YI, Beloozerova IN, Orlovsky GN, Panchin YV, Pavlova GA (1985) Control of locomotion in marine mollusc Clione limacina. i. efferent activity during actual and fictitious swimming. Exp Brain Res 58(2):255–293
go back to reference Arshavsky YI, Grillner S, Orlovsky GN, Panchin YV (1991) Central generators and the spatiotemporal pattern of movements. In: Fagard J, Wolff PH (eds) The development of timing control. Elsevier, Amsterdam, pp 93–115 Arshavsky YI, Grillner S, Orlovsky GN, Panchin YV (1991) Central generators and the spatiotemporal pattern of movements. In: Fagard J, Wolff PH (eds) The development of timing control. Elsevier, Amsterdam, pp 93–115
go back to reference Ashby WR (1960) Design for a brain, 2nd edn. Wiley, New YorkMATH Ashby WR (1960) Design for a brain, 2nd edn. Wiley, New YorkMATH
go back to reference Azouz R, Gray CM (2000) Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo. Proc Natl Acad Sci USA 97(14):8110–8115CrossRef Azouz R, Gray CM (2000) Dynamic spike threshold reveals a mechanism for synaptic coincidence detection in cortical neurons in vivo. Proc Natl Acad Sci USA 97(14):8110–8115CrossRef
go back to reference Barrie JM, Freeman WJ, Lenhart MD (1996) Spatiotemporal analysis of prepyriform, visual, auditory, and somesthetic surface EEGs in trained rabbits. J Neurophysiol 76(1):520–539 Barrie JM, Freeman WJ, Lenhart MD (1996) Spatiotemporal analysis of prepyriform, visual, auditory, and somesthetic surface EEGs in trained rabbits. J Neurophysiol 76(1):520–539
go back to reference Beenhakker MP, Nusbaum MP (2004) Mechanosensory activation of a motor circuit by coactivation of two projection neurons. J Neurosci 24(30):6741–6750CrossRef Beenhakker MP, Nusbaum MP (2004) Mechanosensory activation of a motor circuit by coactivation of two projection neurons. J Neurosci 24(30):6741–6750CrossRef
go back to reference Beggs JM, Plenz D (2003) Neuronal avalanches in neocortical circuits. J Neurosci 23(35):11167–11177 Beggs JM, Plenz D (2003) Neuronal avalanches in neocortical circuits. J Neurosci 23(35):11167–11177
go back to reference Bertram R, Sherman A, Stanley EF (1996) Single-domain/bound calcium hypothesis of transmitter release and facilitation. J Neurophysiol 75(5):1919–1931 Bertram R, Sherman A, Stanley EF (1996) Single-domain/bound calcium hypothesis of transmitter release and facilitation. J Neurophysiol 75(5):1919–1931
go back to reference Brette R et al (2007) Simulation of networks of spiking neurons: a review of tools and strategies. J Comp Neurosci 23(3):349–398MathSciNetCrossRef Brette R et al (2007) Simulation of networks of spiking neurons: a review of tools and strategies. J Comp Neurosci 23(3):349–398MathSciNetCrossRef
go back to reference Buia CI, Tiesinga PHE (2005) Rapid temporal modulation of synchrony in cortical interneuron networks with synaptic plasticity. Computational Neuroscience: Trends in Research 2005. Neurocomputing 6566:809–815CrossRef Buia CI, Tiesinga PHE (2005) Rapid temporal modulation of synchrony in cortical interneuron networks with synaptic plasticity. Computational Neuroscience: Trends in Research 2005. Neurocomputing 6566:809–815CrossRef
go back to reference Cazelles B, Courbage M, Rabinovich MI (2001) Anti-phase regularization of coupled chaotic maps modelling bursting neurons. Europhys Lett 56(4):504–509CrossRef Cazelles B, Courbage M, Rabinovich MI (2001) Anti-phase regularization of coupled chaotic maps modelling bursting neurons. Europhys Lett 56(4):504–509CrossRef
go back to reference Cortes JM, Torres JJ, Marro J, Garrido PL, Kappen HJ (2006) Effects of fast presynaptic noise in attractor neural networks. Neural Comp 18(3):614–633MathSciNetCrossRefMATH Cortes JM, Torres JJ, Marro J, Garrido PL, Kappen HJ (2006) Effects of fast presynaptic noise in attractor neural networks. Neural Comp 18(3):614–633MathSciNetCrossRefMATH
go back to reference Cymbalyuk G, Gaudry O, Masino M, Calabrese R (2002) Bursting in leech heart interneurons: cell-autonomous and network-based mechanisms. J Neurosci 22(24):10580–10592 Cymbalyuk G, Gaudry O, Masino M, Calabrese R (2002) Bursting in leech heart interneurons: cell-autonomous and network-based mechanisms. J Neurosci 22(24):10580–10592
go back to reference Destexhe A, Marder E (2004) Plasticity in single neuron and circuit computations. Nature 431(7010):789–795CrossRef Destexhe A, Marder E (2004) Plasticity in single neuron and circuit computations. Nature 431(7010):789–795CrossRef
go back to reference Destexhe A, Mainen ZF, Sejnowski TJ (1994) An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Comp 6(1):14–18CrossRef Destexhe A, Mainen ZF, Sejnowski TJ (1994) An efficient method for computing synaptic conductances based on a kinetic model of receptor binding. Neural Comp 6(1):14–18CrossRef
go back to reference Dobrunz LE, Stevens CF (1997) Heterogeneity of release probability, facilitation, and depletion at central synapses. Neuron 18(6):995–1008CrossRef Dobrunz LE, Stevens CF (1997) Heterogeneity of release probability, facilitation, and depletion at central synapses. Neuron 18(6):995–1008CrossRef
go back to reference Dyhrfjeld-Johnsen J, Santhakumar V, Morgan RJ, Huerta R, Tsimring L, Soltesz I (2007) Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data. J Neurophysiol 97(2):1566–1587CrossRef Dyhrfjeld-Johnsen J, Santhakumar V, Morgan RJ, Huerta R, Tsimring L, Soltesz I (2007) Topological determinants of epileptogenesis in large-scale structural and functional models of the dentate gyrus derived from experimental data. J Neurophysiol 97(2):1566–1587CrossRef
go back to reference Elson R, Selverston AI, Huerta R, Rabinovich MI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons 81(25):5692–5695 Elson R, Selverston AI, Huerta R, Rabinovich MI, Abarbanel HDI (1998) Synchronous behavior of two coupled biological neurons 81(25):5692–5695
go back to reference Elson R, Huerta R, Abarbanel HDI, Rabinovich MI, Selverston AI (1999) Dynamic control of irregular bursting in an identified neuron of an oscillatory circuit. Phys Rev Lett. J Neurophysiol 82(1):115–122 Elson R, Huerta R, Abarbanel HDI, Rabinovich MI, Selverston AI (1999) Dynamic control of irregular bursting in an identified neuron of an oscillatory circuit. Phys Rev Lett. J Neurophysiol 82(1):115–122
go back to reference FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1(6):445–466CrossRef FitzHugh R (1961) Impulses and physiological states in theoretical models of nerve membrane. Biophys J 1(6):445–466CrossRef
go back to reference Franks KM, Stevens CF, Sejnowski TJ (2003) Independent sources of quantal variability at single glutamatergic synapses. J Neurosci 23(8):3186–3195 Franks KM, Stevens CF, Sejnowski TJ (2003) Independent sources of quantal variability at single glutamatergic synapses. J Neurosci 23(8):3186–3195
go back to reference Freeman W (1972) Progress in theoretical biology, vol 2. Academic, New York Freeman W (1972) Progress in theoretical biology, vol 2. Academic, New York
go back to reference Fusi S, Abbott L (2007) Limits on the memory storage capacity of bounded synapses. Nat Neurosci 10(4):485–493 Fusi S, Abbott L (2007) Limits on the memory storage capacity of bounded synapses. Nat Neurosci 10(4):485–493
go back to reference Garcia-Sanchez M, Huerta R (2003) Design parameters of the fan-out phase of sensory systems. J Comp Neurosci 15(1):5–17CrossRef Garcia-Sanchez M, Huerta R (2003) Design parameters of the fan-out phase of sensory systems. J Comp Neurosci 15(1):5–17CrossRef
go back to reference Getting PA (1989) Emerging principles governing the operation of neural networks. Ann Rev Neurosci 12:185–204CrossRef Getting PA (1989) Emerging principles governing the operation of neural networks. Ann Rev Neurosci 12:185–204CrossRef
go back to reference Gutkin BS, Ermentrout GB (1998) Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanisms and cortical spike train statistics. Neural Comp 10(5):1047–1065CrossRef Gutkin BS, Ermentrout GB (1998) Dynamics of membrane excitability determine interspike interval variability: a link between spike generation mechanisms and cortical spike train statistics. Neural Comp 10(5):1047–1065CrossRef
go back to reference Hebb DO (1949) The organization of behavior. Wiley, New York Hebb DO (1949) The organization of behavior. Wiley, New York
go back to reference Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B 221(1222):87–102CrossRef Hindmarsh JL, Rose RM (1984) A model of neuronal bursting using three coupled first order differential equations. Proc R Soc Lond B 221(1222):87–102CrossRef
go back to reference Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544 Hodgkin AL, Huxley AF (1952) A quantitative description of membrane current and its application to conduction and excitation in nerve. J Physiol 117(4):500–544
go back to reference Holcman D, Tsodyks M (2006) The emergence of up and down states in cortical networks. PLoS Comput Biol 2(3):174–181CrossRef Holcman D, Tsodyks M (2006) The emergence of up and down states in cortical networks. PLoS Comput Biol 2(3):174–181CrossRef
go back to reference Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79(8):2554–2558MathSciNetCrossRef Hopfield JJ (1982) Neural networks and physical systems with emergent collective computational abilities. Proc Natl Acad Sci USA 79(8):2554–2558MathSciNetCrossRef
go back to reference Huerta R, Varona P, Rabinovich MI, Abarbanel HDI (2001) Topology selection by chaotic neurons of a pyloric central pattern generator. Biol Cybern 84(1):L1–L8CrossRef Huerta R, Varona P, Rabinovich MI, Abarbanel HDI (2001) Topology selection by chaotic neurons of a pyloric central pattern generator. Biol Cybern 84(1):L1–L8CrossRef
go back to reference Izhikevich E (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15(5):1063–1070CrossRef Izhikevich E (2004) Which model to use for cortical spiking neurons? IEEE Trans Neural Netw 15(5):1063–1070CrossRef
go back to reference Johnson S, Marro J, Torres JJ (2008) Functional optimization in complex excitable networks. EPL 83:46006(1–6) Johnson S, Marro J, Torres JJ (2008) Functional optimization in complex excitable networks. EPL 83:46006(1–6)
go back to reference Kamiya H, Zucker RS (1994) Residual Ca2+ and short-term synaptic plasticity. Nature 371(6498):603–606CrossRef Kamiya H, Zucker RS (1994) Residual Ca2+ and short-term synaptic plasticity. Nature 371(6498):603–606CrossRef
go back to reference Kandel ER, Schwartz JH, Jessell TM (2000) Principles of neural science, 4th edn. McGraw-Hill, New York, pp 10–11 Kandel ER, Schwartz JH, Jessell TM (2000) Principles of neural science, 4th edn. McGraw-Hill, New York, pp 10–11
go back to reference Kepecs A, Lisman J (2003) Information encoding and computation with spikes and bursts. Network: Comput Neural Syst 14(1):103–118 Kepecs A, Lisman J (2003) Information encoding and computation with spikes and bursts. Network: Comput Neural Syst 14(1):103–118
go back to reference Koch C (1999) Biophysics of computation. Oxford University Press, New York Koch C (1999) Biophysics of computation. Oxford University Press, New York
go back to reference Koch C, Segev I (1998) Methods in neuronal modeling: from ions to networks, 2nd edn. MIT Press, London, pp 6–17 Koch C, Segev I (1998) Methods in neuronal modeling: from ions to networks, 2nd edn. MIT Press, London, pp 6–17
go back to reference Korn H, Faure P (2003) Is there chaos in the brain? II. experimental evidence and related models. C R Biol 326(9):787–840CrossRef Korn H, Faure P (2003) Is there chaos in the brain? II. experimental evidence and related models. C R Biol 326(9):787–840CrossRef
go back to reference Lapicque L (1907) Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarisation. J Physiol Pathol Gen 9:620–635 Lapicque L (1907) Recherches quantitatives sur l’excitation électrique des nerfs traitée comme une polarisation. J Physiol Pathol Gen 9:620–635
go back to reference Laurent G, Stopfer M, Friedrich RW, Rabinovich MI, Volkovskii A, Abarbanel HDO (2001) Odor encoding as an active, dynamical process: experiments, computation, and theory. Annu Rev Neurosci 24:263–297 Laurent G, Stopfer M, Friedrich RW, Rabinovich MI, Volkovskii A, Abarbanel HDO (2001) Odor encoding as an active, dynamical process: experiments, computation, and theory. Annu Rev Neurosci 24:263–297
go back to reference Levi R, Camhi JM (2000) Population vector coding by the giant interneurons of the cockroach. J Neurosci 20(10):3822–3829 Levi R, Camhi JM (2000) Population vector coding by the giant interneurons of the cockroach. J Neurosci 20(10):3822–3829
go back to reference Levi R, Varona P, Arshavsky YI, Rabinovich MI, Selverston AI (2004) Dual sensorymotor function for a molluskan statocyst network. J Neurophysiol 91(1):336–345CrossRef Levi R, Varona P, Arshavsky YI, Rabinovich MI, Selverston AI (2004) Dual sensorymotor function for a molluskan statocyst network. J Neurophysiol 91(1):336–345CrossRef
go back to reference Levi R, Varona P, Arshavsky YI, Rabinovich MI, Selverston AI (2005) The role of sensory network dynamics in generating a motor program. J Neurosci 25(42):9807–9815CrossRef Levi R, Varona P, Arshavsky YI, Rabinovich MI, Selverston AI (2005) The role of sensory network dynamics in generating a motor program. J Neurosci 25(42):9807–9815CrossRef
go back to reference Lewis JE, Kristan WB (1998) Quantitative analysis of a directed behavior in the medicinal leech: implications for organizing motor output. J Neurosci 18(4):1571–1582 Lewis JE, Kristan WB (1998) Quantitative analysis of a directed behavior in the medicinal leech: implications for organizing motor output. J Neurosci 18(4):1571–1582
go back to reference Marder E, Bucher D (2007) Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs. Annu Rev Physiol 69:291–316CrossRef Marder E, Bucher D (2007) Understanding circuit dynamics using the stomatogastric nervous system of lobsters and crabs. Annu Rev Physiol 69:291–316CrossRef
go back to reference Marder E, Calabrese RL (1996) Principles of rhythmic motor pattern generation. Physiol Rev 76(3):687–717 Marder E, Calabrese RL (1996) Principles of rhythmic motor pattern generation. Physiol Rev 76(3):687–717
go back to reference Markram H, Wang Y, Tsodyks M (1998) Differential signaling via the same axon of neocortical pyramidal neurons. Proc Natl Acad Sci USA 95(9):5323–5328CrossRef Markram H, Wang Y, Tsodyks M (1998) Differential signaling via the same axon of neocortical pyramidal neurons. Proc Natl Acad Sci USA 95(9):5323–5328CrossRef
go back to reference Matveev V, Wang XJ (2000) Differential short-term synaptic plasticity and transmission of complex spike trains: to depress or to facilitate? Cerebral Cortex 10(11):1143–1153CrossRef Matveev V, Wang XJ (2000) Differential short-term synaptic plasticity and transmission of complex spike trains: to depress or to facilitate? Cerebral Cortex 10(11):1143–1153CrossRef
go back to reference McAdams C, Maunsell J (1999) Effects of attention on orientation-tuning functions of single neurons in macaque cortical area V4. J Neurosci 19(1):431–441 McAdams C, Maunsell J (1999) Effects of attention on orientation-tuning functions of single neurons in macaque cortical area V4. J Neurosci 19(1):431–441
go back to reference McGraw PM, Menzinger M (2003) Topology and computational performance of attractor neural networks. Phys Rev E 68(4 Pt 2):047102CrossRef McGraw PM, Menzinger M (2003) Topology and computational performance of attractor neural networks. Phys Rev E 68(4 Pt 2):047102CrossRef
go back to reference Mejias JF, Torres JJ (2008) The role of synaptic facilitation in spike coincidence detection. J Comp Neurosci 24(2):222–234CrossRef Mejias JF, Torres JJ (2008) The role of synaptic facilitation in spike coincidence detection. J Comp Neurosci 24(2):222–234CrossRef
go back to reference Mejias JF, Torres JJ (2009) Maximum memory capacity on neural networks with short-term synaptic depression and facilitation. Neural Comput 21(3):851–871MathSciNetCrossRefMATH Mejias JF, Torres JJ (2009) Maximum memory capacity on neural networks with short-term synaptic depression and facilitation. Neural Comput 21(3):851–871MathSciNetCrossRefMATH
go back to reference Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35(1):193–213CrossRef Morris C, Lecar H (1981) Voltage oscillations in the barnacle giant muscle fiber. Biophys J 35(1):193–213CrossRef
go back to reference Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50:2061–2070CrossRef Nagumo J, Arimoto S, Yoshizawa S (1962) An active pulse transmission line simulating nerve axon. Proc IRE 50:2061–2070CrossRef
go back to reference Nowotny T, Huerta R (2003) Explaining synchrony in feed-forward networks: are McCulloch-Pitts neurons good enough? Biol Cybern 89(4):237–241CrossRefMATH Nowotny T, Huerta R (2003) Explaining synchrony in feed-forward networks: are McCulloch-Pitts neurons good enough? Biol Cybern 89(4):237–241CrossRefMATH
go back to reference Panchin YV, Arshavsky YI, Deliagina TG, Popova LB, Orlovsky GN (1995) Control of locomotion in marine mollusk Clione limacina. ix. neuronal mechanisms of spatial orientation. J Neurophysiol 75(5):1924–1936 Panchin YV, Arshavsky YI, Deliagina TG, Popova LB, Orlovsky GN (1995) Control of locomotion in marine mollusk Clione limacina. ix. neuronal mechanisms of spatial orientation. J Neurophysiol 75(5):1924–1936
go back to reference Pantic L, Torres JJ, Kappen HJ, Gielen SCA (2002) Associative memory with dynamic synapses. Neural Comp 14(12):2903–2923CrossRefMATH Pantic L, Torres JJ, Kappen HJ, Gielen SCA (2002) Associative memory with dynamic synapses. Neural Comp 14(12):2903–2923CrossRefMATH
go back to reference Peretto P (1992) An introduction to the modeling of neural networks. Cambridge University Press, CambridgeCrossRefMATH Peretto P (1992) An introduction to the modeling of neural networks. Cambridge University Press, CambridgeCrossRefMATH
go back to reference Pinault D, Smith Y, Deschnes M (1997) Dendrodendritic and axoaxonic synapses in the thalamic reticular nucleus of the adult rat. J Neurosci 17(9):3215–3233 Pinault D, Smith Y, Deschnes M (1997) Dendrodendritic and axoaxonic synapses in the thalamic reticular nucleus of the adult rat. J Neurosci 17(9):3215–3233
go back to reference Pinto RD, Varona P, Volkovskii AR, Szucs A, Abarbanel HD, Rabinovich MI (2000) Synchronous behavior of two coupled electronic neurons. Phys Rev E 62(2 Pt B):2644–2656CrossRef Pinto RD, Varona P, Volkovskii AR, Szucs A, Abarbanel HD, Rabinovich MI (2000) Synchronous behavior of two coupled electronic neurons. Phys Rev E 62(2 Pt B):2644–2656CrossRef
go back to reference Prinz A (2006) Insights from models of rhythmic motor systems. Curr Opin Neurobiol 16(6):615–620CrossRef Prinz A (2006) Insights from models of rhythmic motor systems. Curr Opin Neurobiol 16(6):615–620CrossRef
go back to reference Rabinovich MI, Varona P, Selverston AI, Abarbanel HDI (2006) Dynamical principles in neuroscience. Rev Mod Phys 78:1213–1265CrossRef Rabinovich MI, Varona P, Selverston AI, Abarbanel HDI (2006) Dynamical principles in neuroscience. Rev Mod Phys 78:1213–1265CrossRef
go back to reference Rabinovich MI, Huerta R, Varona P, Afraimovich VS (2008) Transient cognitive dynamics, metastability, and decision making. PLoS Comput Biol 4(5):e1000072MathSciNetCrossRef Rabinovich MI, Huerta R, Varona P, Afraimovich VS (2008) Transient cognitive dynamics, metastability, and decision making. PLoS Comput Biol 4(5):e1000072MathSciNetCrossRef
go back to reference Ramirez J, Tryba A, Pena F (2004) Pacemaker neurons and neuronal networks: an integrative view. Curr Opin Neurobiol 6(6):665–674CrossRef Ramirez J, Tryba A, Pena F (2004) Pacemaker neurons and neuronal networks: an integrative view. Curr Opin Neurobiol 6(6):665–674CrossRef
go back to reference Reyes MB, Huerta R, Rabinovich MI, Selverston AI (2003) Artificial synaptic modification reveals a dynamical invariant in the pyloric CPG. Eur J Appl Physiol 102(6):667–675CrossRef Reyes MB, Huerta R, Rabinovich MI, Selverston AI (2003) Artificial synaptic modification reveals a dynamical invariant in the pyloric CPG. Eur J Appl Physiol 102(6):667–675CrossRef
go back to reference Rosenblatt F (1962) Principles of neurodynamics: perceptions and the theory of brain mechanisms. Spartan Books, New York Rosenblatt F (1962) Principles of neurodynamics: perceptions and the theory of brain mechanisms. Spartan Books, New York
go back to reference Roxin A, Riecke H, Solla SA (2004) Self-sustained activity in a small-world network of excitable neurons. Phys Rev Lett 92(19):198101CrossRef Roxin A, Riecke H, Solla SA (2004) Self-sustained activity in a small-world network of excitable neurons. Phys Rev Lett 92(19):198101CrossRef
go back to reference Rulkov NF (2001) Regularization of synchronized chaotic bursts. Phys Rev Lett 86(1):183–186CrossRef Rulkov NF (2001) Regularization of synchronized chaotic bursts. Phys Rev Lett 86(1):183–186CrossRef
go back to reference Rulkov NF (2002) Modeling of spiking-bursting neural behavior using two-dimensional map. Phys Rev E 65(4 Pt 1):041922MathSciNetCrossRef Rulkov NF (2002) Modeling of spiking-bursting neural behavior using two-dimensional map. Phys Rev E 65(4 Pt 1):041922MathSciNetCrossRef
go back to reference Selverston A (2005) A neural infrastructure for rhythmic motor patterns. Cell Mol Neurobiol 25(2):223–244CrossRef Selverston A (2005) A neural infrastructure for rhythmic motor patterns. Cell Mol Neurobiol 25(2):223–244CrossRef
go back to reference Selverston AI, Moulins M (eds) (1987) The crustacean stomatogastric system. Springer, Berlin Selverston AI, Moulins M (eds) (1987) The crustacean stomatogastric system. Springer, Berlin
go back to reference Selverston AI, Rabinovich MI, Abarbanel HDI, Elson R, Szcs A, Pinto RD, Huerta R, Varona P (2000) Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators. J Physiol (Paris) 94(5–6):357–374CrossRef Selverston AI, Rabinovich MI, Abarbanel HDI, Elson R, Szcs A, Pinto RD, Huerta R, Varona P (2000) Reliable circuits from irregular neurons: a dynamical approach to understanding central pattern generators. J Physiol (Paris) 94(5–6):357–374CrossRef
go back to reference Simmers AJ, Moulins M (1988) A disynaptic sensorimotor pathway in the lobster stomatogastric system. J Neurophysiol 59(3):740–756 Simmers AJ, Moulins M (1988) A disynaptic sensorimotor pathway in the lobster stomatogastric system. J Neurophysiol 59(3):740–756
go back to reference Stein SG, Grillner S, Selverston AI, Douglas GS (eds) (1997) Neurons, networks, and motor behavior. MIT Press, Cambridge Stein SG, Grillner S, Selverston AI, Douglas GS (eds) (1997) Neurons, networks, and motor behavior. MIT Press, Cambridge
go back to reference Stiesberg GR, Reyes MB, Varona P, Pinto RD, Huerta R (2007) Connection topology selection in central pattern generators by maximizing the gain of information. Neural Comp 19(4):974–993CrossRefMATH Stiesberg GR, Reyes MB, Varona P, Pinto RD, Huerta R (2007) Connection topology selection in central pattern generators by maximizing the gain of information. Neural Comp 19(4):974–993CrossRefMATH
go back to reference Swiercz W, Cios KJ, Staley K, Kurgan L, Accurso F, Sagel S (2006) A new synaptic plasticity rule for networks of spiking neurons. IEEE Trans Neural Netw 17(1):94–105CrossRef Swiercz W, Cios KJ, Staley K, Kurgan L, Accurso F, Sagel S (2006) A new synaptic plasticity rule for networks of spiking neurons. IEEE Trans Neural Netw 17(1):94–105CrossRef
go back to reference Szucs A, Varona P, Volkovskii AR, Abarbanel HD, Rabinovich MI, Selverston AI (2000) Interacting biological and electronic neurons generate realistic oscillatory rhythms. Neuroreport 11(11):563–569CrossRef Szucs A, Varona P, Volkovskii AR, Abarbanel HD, Rabinovich MI, Selverston AI (2000) Interacting biological and electronic neurons generate realistic oscillatory rhythms. Neuroreport 11(11):563–569CrossRef
go back to reference Szucs A, Pinto RD, Rabinovich MI, Abarbanel HD, Selverston AI (2003) Synaptic modulation of the interspike interval signatures of bursting pyloric neurons. J Neurophysiol 89(3):1363–1377CrossRef Szucs A, Pinto RD, Rabinovich MI, Abarbanel HD, Selverston AI (2003) Synaptic modulation of the interspike interval signatures of bursting pyloric neurons. J Neurophysiol 89(3):1363–1377CrossRef
go back to reference Torres JJ, Munoz MA, Marro J, Garrido PL (2004) Influence of topology on the performance of a neural network. Computational Neuroscience: Trends in Research. 58–60:229–234CrossRef Torres JJ, Munoz MA, Marro J, Garrido PL (2004) Influence of topology on the performance of a neural network. Computational Neuroscience: Trends in Research. 58–60:229–234CrossRef
go back to reference Torres JJ, Cortes JM, Marro J (2007a) Information processing with unstable memories. Neurocomputing AIP Conf Proc 887:115–128MathSciNetCrossRef Torres JJ, Cortes JM, Marro J (2007a) Information processing with unstable memories. Neurocomputing AIP Conf Proc 887:115–128MathSciNetCrossRef
go back to reference Torres JJ, Cortes JM, Marro J, Kappen HJ (2007b) Competition between synaptic depression and facilitation in attractor neural networks. Neural Comp 19(10):2739–2755MathSciNetCrossRefMATH Torres JJ, Cortes JM, Marro J, Kappen HJ (2007b) Competition between synaptic depression and facilitation in attractor neural networks. Neural Comp 19(10):2739–2755MathSciNetCrossRefMATH
go back to reference Tsodyks M, Feigelman M (1988) The enhanced storage capacity in neural networks with low activity level. Europhys Lett 6:101–105CrossRef Tsodyks M, Feigelman M (1988) The enhanced storage capacity in neural networks with low activity level. Europhys Lett 6:101–105CrossRef
go back to reference Tsodyks MV, Markram H (1997) The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc Natl Acad Sci USA 94(2):719–723CrossRef Tsodyks MV, Markram H (1997) The neural code between neocortical pyramidal neurons depends on neurotransmitter release probability. Proc Natl Acad Sci USA 94(2):719–723CrossRef
go back to reference Tsodyks MV, Pawelzik K, Markram H (1998) Neural networks with dynamic synapses. Neural Comp 10(4):821–835CrossRef Tsodyks MV, Pawelzik K, Markram H (1998) Neural networks with dynamic synapses. Neural Comp 10(4):821–835CrossRef
go back to reference Varona P, Ibarz JM, López L, Herreras O (2000) Macroscopic and subcellular factors shaping population spikes. J Neurophysiol 83(4):2192–2208 Varona P, Ibarz JM, López L, Herreras O (2000) Macroscopic and subcellular factors shaping population spikes. J Neurophysiol 83(4):2192–2208
go back to reference Varona P, Torres JJ, Huerta R, Abarbanel HDI, Rabinovich MI (2001a) Regularization mechanisms of spiking-bursting neurons. Neural Netw 14(6–7):865–875CrossRef Varona P, Torres JJ, Huerta R, Abarbanel HDI, Rabinovich MI (2001a) Regularization mechanisms of spiking-bursting neurons. Neural Netw 14(6–7):865–875CrossRef
go back to reference Varona P, Torres JJ, Abarbanel HDI, Rabinovich MI, Elson RC (2001b) Dynamics of two electrically coupled chaotic neurons: experimental observations and model analysis. Biol Cybern 84(2):91–101CrossRef Varona P, Torres JJ, Abarbanel HDI, Rabinovich MI, Elson RC (2001b) Dynamics of two electrically coupled chaotic neurons: experimental observations and model analysis. Biol Cybern 84(2):91–101CrossRef
go back to reference Varona P, Rabinovich MI, Selverston AI, Arshavsky YI (2002) Winnerless competition between sensory neurons generates chaos: a possible mechanism for molluscan hunting behavior. Chaos 12(3):672–677MathSciNetCrossRefMATH Varona P, Rabinovich MI, Selverston AI, Arshavsky YI (2002) Winnerless competition between sensory neurons generates chaos: a possible mechanism for molluscan hunting behavior. Chaos 12(3):672–677MathSciNetCrossRefMATH
go back to reference von der Malsburg C (1981) The correlation theory of brain function. MPI Biophysical Chemistry, Internal Report von der Malsburg C (1981) The correlation theory of brain function. MPI Biophysical Chemistry, Internal Report
go back to reference Zeck GM, Masland RH (2007) Spike train signatures of retinal ganglion cell types. Eur J Neurosci 26(2):367–380CrossRef Zeck GM, Masland RH (2007) Spike train signatures of retinal ganglion cell types. Eur J Neurosci 26(2):367–380CrossRef
Metadata
Title
Modeling Biological Neural Networks
Authors
Joaquin J. Torres
Pablo Varona
Copyright Year
2012
Publisher
Springer Berlin Heidelberg
DOI
https://doi.org/10.1007/978-3-540-92910-9_17

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