메뉴 건너뛰기




Volumn 6, Issue 12 A/B, 1996, Pages 2343-2360

Modeling neurons by simple maps

Author keywords

[No Author keywords available]

Indexed keywords


EID: 0347878125     PISSN: 02181274     EISSN: None     Source Type: Journal    
DOI: 10.1142/s0218127496001508     Document Type: Article
Times cited : (36)

References (61)
  • 1
    • 0000411741 scopus 로고
    • A network of oscillators
    • Abbott, L. F. [1990] "A network of oscillators," J. Phys. A: Math. Gen. 23, 3835-3859.
    • (1990) J. Phys. A: Math. Gen. , vol.23 , pp. 3835-3859
    • Abbott, L.F.1
  • 2
    • 22244458151 scopus 로고
    • Asynchronous states in networks of pulse-coupled oscillators
    • Abbott, L. F. & van Vreeswijk, C. [1993] "Asynchronous states in networks of pulse-coupled oscillators," Phys. Rev. E48, 1483-1490.
    • (1993) Phys. Rev. , vol.E48 , pp. 1483-1490
    • Abbott, L.F.1    Van Vreeswijk, C.2
  • 4
    • 84957320212 scopus 로고
    • Phase locking in a network of neural oscillators
    • Arenas, A. & Pérez Vicente, C. J. [1994] "Phase locking in a network of neural oscillators," Europhys. Lett. 26, 79-83.
    • (1994) Europhys. Lett. , vol.26 , pp. 79-83
    • Arenas, A.1    Pérez Vicente, C.J.2
  • 5
    • 0000788823 scopus 로고
    • Ising model with solitons, phasons and the devil's staircase
    • Bak, P. & von Boehm, J. [1980] "Ising model with solitons, phasons and the devil's staircase," Phys. Rev. B21, 5297-5308.
    • (1980) Phys. Rev. , vol.B21 , pp. 5297-5308
    • Bak, P.1    Von Boehm, J.2
  • 6
    • 0018774718 scopus 로고
    • Null space in the Hodgkin-Huxley equations: A critical test
    • Best, E. N. [1979] "Null space in the Hodgkin-Huxley equations: A critical test," Biophys. J. 27, 87-104.
    • (1979) Biophys. J. , vol.27 , pp. 87-104
    • Best, E.N.1
  • 7
    • 0001689540 scopus 로고    scopus 로고
    • Marginally stable swarms are flexible and efficient
    • Bonabeau, E. [1996] "Marginally stable swarms are flexible and efficient," J. Phys. I France 6, 309-324.
    • (1996) J. Phys. I France , vol.6 , pp. 309-324
    • Bonabeau, E.1
  • 8
    • 0040890382 scopus 로고
    • Collective behaviors in coupled map lattices with local and non local connections
    • Chaté, H. & Manneville, P. [1992] "Collective behaviors in coupled map lattices with local and non local connections," Chaos 2, 307-313.
    • (1992) Chaos , vol.2 , pp. 307-313
    • Chaté, H.1    Manneville, P.2
  • 9
    • 21144478251 scopus 로고
    • Modulated noisy biological dynamics: Three examples
    • Chialvo, D. R. & Apkarian, A. V. [1993] "Modulated noisy biological dynamics: Three examples," J. Statistical Physics 70, 375-391.
    • (1993) J. Statistical Physics , vol.70 , pp. 375-391
    • Chialvo, D.R.1    Apkarian, A.V.2
  • 10
    • 0000492003 scopus 로고
    • Generic excitable dynamics on a two-dimensional map
    • Chialvo, D. R. [1995] "Generic excitable dynamics on a two-dimensional map," Chaos, Solitons and Fractals 5, 461-480.
    • (1995) Chaos, Solitons and Fractals , vol.5 , pp. 461-480
    • Chialvo, D.R.1
  • 11
    • 0002026089 scopus 로고
    • Possible neural mechanisms of feature linking in the visual system. Stimulus-locked and stimulus-induced synchronizations
    • ed. Babloyantz, A. (Plenum Press, New York)
    • Eckhorn, R. & Schanze, T. [1991] "Possible neural mechanisms of feature linking in the visual system. Stimulus-locked and stimulus-induced synchronizations," in Self-Organization, Emerging Properties, and Learning, ed. Babloyantz, A. (Plenum Press, New York), pp. 63-80.
    • (1991) Self-Organization, Emerging Properties, and Learning , pp. 63-80
    • Eckhorn, R.1    Schanze, T.2
  • 12
    • 0000368783 scopus 로고
    • Synchronization induced by temporal delays in pulse-coupled oscillators
    • Ernst, U., Pawelzik, K. & Geisel, T. [1995] "Synchronization induced by temporal delays in pulse-coupled oscillators," Phys. Rev. Lett. 74, 1570-1573.
    • (1995) Phys. Rev. Lett. , vol.74 , pp. 1570-1573
    • Ernst, U.1    Pawelzik, K.2    Geisel, T.3
  • 13
    • 0027625581 scopus 로고
    • Bifurcations, burstings chaos and crisis in the Rose-Hindmarsh model for neuronal activity
    • Fan, Y. & Holden, A. V. [1993] "Bifurcations, burstings chaos and crisis in the Rose-Hindmarsh model for neuronal activity," Chaos, Solitons and Fractals 3, 132-143.
    • (1993) Chaos, Solitons and Fractals , vol.3 , pp. 132-143
    • Fan, Y.1    Holden, A.V.2
  • 14
    • 0000450921 scopus 로고
    • Thresholds and plateaus in the Hodgkin-Huxley nerve equations
    • FitzHugh, R. [1960] "Thresholds and plateaus in the Hodgkin-Huxley nerve equations," J. Gen. Physiol. 43, 867-896.
    • (1960) J. Gen. Physiol. , vol.43 , pp. 867-896
    • FitzHugh, R.1
  • 15
    • 0025328346 scopus 로고
    • Odour-modulated collective network oscillations of olfatory interneurons in a terrestrial mollusc
    • Gelperin, A. & Tank, D. W. [1990] "Odour-modulated collective network oscillations of olfatory interneurons in a terrestrial mollusc," Nature 345, 437-440.
    • (1990) Nature , vol.345 , pp. 437-440
    • Gelperin, A.1    Tank, D.W.2
  • 16
    • 0000379808 scopus 로고
    • Coherence and incoherence in a globally coupled ensemble of pulse-emitting units
    • Gerstner, W. & van Hemmen, J. L. [1993] "Coherence and incoherence in a globally coupled ensemble of pulse-emitting units," Phys. Rev. Lett. 71, 312-315.
    • (1993) Phys. Rev. Lett. , vol.71 , pp. 312-315
    • Gerstner, W.1    Van Hemmen, J.L.2
  • 17
    • 0001297707 scopus 로고
    • Dynamics of globally inhibitory neurons with heterogeneity
    • Golomb, D. & Rinzel, J. [1993] "Dynamics of globally inhibitory neurons with heterogeneity," Phys. Rev. E48, 4810-4814.
    • (1993) Phys. Rev. , vol.E48 , pp. 4810-4814
    • Golomb, D.1    Rinzel, J.2
  • 18
    • 0001075269 scopus 로고
    • Stability in asymmetric Hopfield nets with transmission delays
    • Gopalsamy, K. & He, X. [1994] "Stability in asymmetric Hopfield nets with transmission delays," Physica D76, 344-358.
    • (1994) Physica , vol.D76 , pp. 344-358
    • Gopalsamy, K.1    He, X.2
  • 19
    • 0024514737 scopus 로고
    • Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties
    • Gray, C. M., Konig, P., Engel, A. K. & Singer, W. [1989] "Oscillatory responses in cat visual cortex exhibit inter-columnar synchronization which reflects global stimulus properties," Nature 338, 334-337.
    • (1989) Nature , vol.338 , pp. 334-337
    • Gray, C.M.1    Konig, P.2    Engel, A.K.3    Singer, W.4
  • 20
    • 11944256929 scopus 로고
    • Synchronization and computation in a chaotic neural network
    • Hansel, D. & Sompolinsky, H. [1992] "Synchronization and computation in a chaotic neural network," Phys. Rev. Lett. 68, 718-721.
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 718-721
    • Hansel, D.1    Sompolinsky, H.2
  • 22
    • 0001583955 scopus 로고
    • Statistical mechanics of temporal association in neural networks with transmission delays
    • Herz, A. V. M., Li, Z. & van Hemmen, J. L. [1991] "Statistical mechanics of temporal association in neural networks with transmission delays," Phys. Rev. Lett. 66, 1370-1373.
    • (1991) Phys. Rev. Lett. , vol.66 , pp. 1370-1373
    • Herz, A.V.M.1    Li, Z.2    Van Hemmen, J.L.3
  • 23
    • 11944266612 scopus 로고
    • Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements
    • Herz, A. V. M. & Hopfield, J. J. [1995] "Earthquake cycles and neural reverberations: Collective oscillations in systems with pulse-coupled threshold elements," Phys. Rev. Lett. 75, 1222-1225.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 1222-1225
    • Herz, A.V.M.1    Hopfield, J.J.2
  • 24
    • 0008982810 scopus 로고
    • Networks of complex neurons
    • Horn, D. [1993] "Networks of complex neurons," Physica A200, 594-601.
    • (1993) Physica , vol.A200 , pp. 594-601
    • Horn, D.1
  • 25
    • 0004469897 scopus 로고
    • Neurons with graded response have collective computational properties like those of two-state neurons
    • Hopfield, J. J. [1984] "Neurons with graded response have collective computational properties like those of two-state neurons," Proc. Natl. Acad. Sci. USA 81, 3088-3092.
    • (1984) Proc. Natl. Acad. Sci. USA , vol.81 , pp. 3088-3092
    • Hopfield, J.J.1
  • 26
    • 0000429378 scopus 로고
    • Analytical study of time series generation by feed-forward networks
    • Kanter, I., Kessler, A., Priel, A. & Eisenstein, E. [1995] "Analytical study of time series generation by feed-forward networks," Phys. Rev. Lett. 75, 2614-2617.
    • (1995) Phys. Rev. Lett. , vol.75 , pp. 2614-2617
    • Kanter, I.1    Kessler, A.2    Priel, A.3    Eisenstein, E.4
  • 27
    • 0002215637 scopus 로고
    • Relevance of dynamic clustering to biological networks
    • Kaneko, K. [1994] "Relevance of dynamic clustering to biological networks," Physica D75, 55-73.
    • (1994) Physica , vol.D75 , pp. 55-73
    • Kaneko, K.1
  • 29
  • 30
    • 38249005933 scopus 로고
    • The behavior of the Lyapunov exponent of a map simulating neural activity
    • Làbos, E., Holden, A. V. & Zhang, H. [1993] "The behavior of the Lyapunov exponent of a map simulating neural activity," Phys. Lett. A173, 399-406.
    • (1993) Phys. Lett. , vol.A173 , pp. 399-406
    • Làbos, E.1    Holden, A.V.2    Zhang, H.3
  • 31
    • 0001631287 scopus 로고
    • Studying artificial life with cellular automata
    • Langton, C. G. [1986] "Studying artificial life with cellular automata," Physica D22, 120-149.
    • (1986) Physica , vol.D22 , pp. 120-149
    • Langton, C.G.1
  • 32
    • 21844510737 scopus 로고
    • Quasiperiodicity and bifurcation phenomena in Ising spin neural networks with asymmetric interaction
    • Laughton, S. N. & Coolen, A. C. C. [1994] "Quasiperiodicity and bifurcation phenomena in Ising spin neural networks with asymmetric interaction," J. Phys. A: Math. Gen. 27, 8011-8028.
    • (1994) J. Phys. A: Math. Gen. , vol.27 , pp. 8011-8028
    • Laughton, S.N.1    Coolen, A.C.C.2
  • 33
    • 0027960120 scopus 로고
    • Encoding of olfactory information with oscillating neural assemblies
    • Laurent, G. & Davidowitz, H. [1994] "Encoding of olfactory information with oscillating neural assemblies," Science 265, 1872-1875.
    • (1994) Science , vol.265 , pp. 1872-1875
    • Laurent, G.1    Davidowitz, H.2
  • 34
    • 0024239764 scopus 로고
    • The intrinsic electrophysiological properties of mammalian neurons: Insights into central nervous system function
    • Llinas, R. R. [1988] "The intrinsic electrophysiological properties of mammalian neurons: Insights into central nervous system function," Science 242, 1654-1664.
    • (1988) Science , vol.242 , pp. 1654-1664
    • Llinas, R.R.1
  • 35
    • 0000414517 scopus 로고
    • Associative memory in an analog iterated map neural network
    • Marcus, C. M., Waugh, F. R. & Westervelt, R. M. [1990] "Associative memory in an analog iterated map neural network," Phys. Rev. A41, 3355-3364.
    • (1990) Phys. Rev. , vol.A41 , pp. 3355-3364
    • Marcus, C.M.1    Waugh, F.R.2    Westervelt, R.M.3
  • 36
    • 0000380827 scopus 로고
    • Nonlinear dynamics and stability of analog neural networks
    • Marcus, C. M., Waugh, F. R. & Westervelt, R. M. [1991] "Nonlinear dynamics and stability of analog neural networks," Physica D51, 234-247.
    • (1991) Physica , vol.D51 , pp. 234-247
    • Marcus, C.M.1    Waugh, F.R.2    Westervelt, R.M.3
  • 37
    • 0346578393 scopus 로고
    • Critical slowingdown near the transition region from the resting to time-ordered states in squid giant axons
    • Matsumoto, G. & Kunisawa, T. [1978] "Critical slowingdown near the transition region from the resting to time-ordered states in squid giant axons," J. Phys. Soc. Japan 44, 1047-1048.
    • (1978) J. Phys. Soc. Japan , vol.44 , pp. 1047-1048
    • Matsumoto, G.1    Kunisawa, T.2
  • 38
  • 39
    • 0019405994 scopus 로고
    • Voltage oscillations in the barnacle giant muscle fiber
    • Morris, C. & Lecar, H. [1981] "Voltage oscillations in the barnacle giant muscle fiber," Biophys. J. 35, 193-213.
    • (1981) Biophys. J. , vol.35 , pp. 193-213
    • Morris, C.1    Lecar, H.2
  • 40
    • 4243856764 scopus 로고
    • Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes
    • Olami, Z., Feder, H. J. S. & Christensen, K. [1992] "Self-organized criticality in a continuous, nonconservative cellular automaton modeling earthquakes," Phys. Rev. Lett. 68, 1244-1247.
    • (1992) Phys. Rev. Lett. , vol.68 , pp. 1244-1247
    • Olami, Z.1    Feder, H.J.S.2    Christensen, K.3
  • 41
    • 21344493947 scopus 로고
    • Dynamics of a single model neuron
    • Pasemann, F. [1993a] "Dynamics of a single model neuron," Int. J. Bifurcation and Chaos 3, 271-278.
    • (1993) Int. J. Bifurcation and Chaos , vol.3 , pp. 271-278
    • Pasemann, F.1
  • 42
    • 0011680288 scopus 로고
    • Elements of nonconvergent neurodynamics
    • eds. Andersson, S., Andersson, A. & Ottoson, U. (World Scientific, Singapore)
    • Pasemann, F. [1993b] "Elements of nonconvergent neurodynamics," in Dynamical Systems -Theory and Applications, eds. Andersson, S., Andersson, A. & Ottoson, U. (World Scientific, Singapore), pp. 167-201.
    • (1993) Dynamical Systems -Theory and Applications , pp. 167-201
    • Pasemann, F.1
  • 43
    • 0040890874 scopus 로고    scopus 로고
    • On self-organized criticality and synchronization in lattice models of coupled dynamical systems
    • Perez, C. J., Corral, A., Díaz-Guilera, A., Christensen, K. & Arenas, A. [1996] "On self-organized criticality and synchronization in lattice models of coupled dynamical systems," Int. J. Mod. Phys. B10, 1111-1151.
    • (1996) Int. J. Mod. Phys. , vol.B10 , pp. 1111-1151
    • Perez, C.J.1    Corral, A.2    Díaz-Guilera, A.3    Christensen, K.4    Arenas, A.5
  • 44
    • 84956234201 scopus 로고
    • Nonstandard Farey sequences in a realistic diode map
    • Perez, G., Sinha, S. & Cerdeira, H. A. [1991] "Nonstandard Farey sequences in a realistic diode map," Europhys. Lett. 16, 635-641.
    • (1991) Europhys. Lett. , vol.16 , pp. 635-641
    • Perez, G.1    Sinha, S.2    Cerdeira, H.A.3
  • 45
    • 0346578392 scopus 로고
    • Dimensions of a strange attractor associated with the Ising model with competing interactions
    • Prado, C. P. C. & Fiedler-Ferrari, N. [1989] "Dimensions of a strange attractor associated with the Ising model with competing interactions," Phys. Lett. A135, 175-178.
    • (1989) Phys. Lett. , vol.A135 , pp. 175-178
    • Prado, C.P.C.1    Fiedler-Ferrari, N.2
  • 46
    • 0022001098 scopus 로고
    • A model of a thalamic neuron
    • Rose, R. M. & Hindmarsh, J. L. [1985] "A model of a thalamic neuron," Proc. R. Soc. B25, 161-193.
    • (1985) Proc. R. Soc. , vol.B25 , pp. 161-193
    • Rose, R.M.1    Hindmarsh, J.L.2
  • 47
    • 84973949757 scopus 로고
    • How brains make chaos in order to make sense of the world
    • Skarda, C. A. & Freeman, W. J. [1987] "How brains make chaos in order to make sense of the world," Behavior. Brain Sci. 10, 161-195.
    • (1987) Behavior. Brain Sci. , vol.10 , pp. 161-195
    • Skarda, C.A.1    Freeman, W.J.2
  • 48
    • 0001761129 scopus 로고
    • Cooperative dynamics in visual processing
    • Sompolinsky, H., Golomb, D. & Kleinfeld, D. [1991] "Cooperative dynamics in visual processing," Phys. Rev. A43, 6990-7011.
    • (1991) Phys. Rev. , vol.A43 , pp. 6990-7011
    • Sompolinsky, H.1    Golomb, D.2    Kleinfeld, D.3
  • 49
    • 0040548819 scopus 로고
    • Critical phase transitions made self-organized: A dynamical system feedback mechanism for self-organized criticality
    • Sornette, D. [1992] "Critical phase transitions made self-organized: A dynamical system feedback mechanism for self-organized criticality," J. Phys. I France 2, 2065-2073.
    • (1992) J. Phys. I France , vol.2 , pp. 2065-2073
    • Sornette, D.1
  • 50
    • 26344435590 scopus 로고    scopus 로고
    • Dynamical phase diagrams of neural networks with asymmetric couplings
    • to appear
    • Tamashiro, M. N., Kinouchi, O. & Salinas, S. R. A. [1996] "Dynamical phase diagrams of neural networks with asymmetric couplings," to appear in Phys. Rev. E.
    • (1996) Phys. Rev. E
    • Tamashiro, M.N.1    Kinouchi, O.2    Salinas, S.R.A.3
  • 51
    • 0000937689 scopus 로고
    • Demonstration of two stable potential states in the squid giant axon under tetraethylammonium chloride
    • Tasaki, I. & Hagiwara, S. [1957] "Demonstration of two stable potential states in the squid giant axon under tetraethylammonium chloride," J. Gen. Physiol. 40, 859-862.
    • (1957) J. Gen. Physiol. , vol.40 , pp. 859-862
    • Tasaki, I.1    Hagiwara, S.2
  • 52
    • 0000862074 scopus 로고
    • Field behavior of an Ising model with competing interactions on the Bethe lattice
    • Tragtenberg, M. H. R. & Yokoi C. S. O. [1995] "Field behavior of an Ising model with competing interactions on the Bethe lattice," Phys. Rev. E52, 2187-2197.
    • (1995) Phys. Rev. , vol.E52 , pp. 2187-2197
    • Tragtenberg, M.H.R.1    Yokoi, C.S.O.2
  • 54
    • 0016962434 scopus 로고
    • Bifurcation phenomena in FitzHugh's nerve conduction equations
    • Troy, W. C. [1976] "Bifurcation phenomena in FitzHugh's nerve conduction equations," J. Math. Anal. Appl. 54, 678-690.
    • (1976) J. Math. Anal. Appl. , vol.54 , pp. 678-690
    • Troy, W.C.1
  • 55
    • 0011837322 scopus 로고
    • The bifurcation of periodic solutions in the Hodgkin-Huxley equations
    • Troy, W. C. [1978] "The bifurcation of periodic solutions in the Hodgkin-Huxley equations," Quart. Appl. Math. 36, 73-83.
    • (1978) Quart. Appl. Math. , vol.36 , pp. 73-83
    • Troy, W.C.1
  • 56
    • 0028392406 scopus 로고
    • Locally recurrent globally feedforward networks: A critical review of architectures
    • Tsoi, A. C. & Back, A. D. [1994] "Locally recurrent globally feedforward networks: A critical review of architectures," IEEE Trans. N. Networks 5, 229-239.
    • (1994) IEEE Trans. N. Networks , vol.5 , pp. 229-239
    • Tsoi, A.C.1    Back, A.D.2
  • 58
    • 21144473858 scopus 로고
    • Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators
    • van Hemmen, J. L. & Wreszinski, W. F. [1993] "Lyapunov function for the Kuramoto model of nonlinearly coupled oscillators," J. Stat. Phys. 72, 145-166.
    • (1993) J. Stat. Phys. , vol.72 , pp. 145-166
    • Hemmen, J.L.1    Wreszinski, W.F.2
  • 59
    • 21344493445 scopus 로고
    • Spatial, temporal, and global mode entropy in a thalamo-cortical network
    • Wallenstein, G. V. [1993] "Spatial, temporal, and global mode entropy in a thalamo-cortical network," Int. J. Bifurcation and Chaos 3, 1487-1501.
    • (1993) Int. J. Bifurcation and Chaos , vol.3 , pp. 1487-1501
    • Wallenstein, G.V.1
  • 60
    • 26344477421 scopus 로고
    • Chiral potts model on a Cayley tree with complete and incomplete devil's staircase
    • Yokoi, C. S. O. & de Oliveira, M. J. [1985] "Chiral potts model on a Cayley tree with complete and incomplete devil's staircase," J. Phys. A: Math. Gen. 18, L153-L157.
    • (1985) J. Phys. A: Math. Gen. , vol.18
    • Yokoi, C.S.O.1    De Oliveira, M.J.2
  • 61
    • 4243091335 scopus 로고
    • Strange attractor in the Ising model with competing interactions on the Cayley tree
    • Yokoi, C. S. O., de Oliveira, M. J. & Salinas, S. R. [1985] "Strange attractor in the Ising model with competing interactions on the Cayley tree," Phys. Rev. Lett. 54, 163-166.
    • (1985) Phys. Rev. Lett. , vol.54 , pp. 163-166
    • Yokoi, C.S.O.1    De Oliveira, M.J.2    Salinas, S.R.3


* 이 정보는 Elsevier사의 SCOPUS DB에서 KISTI가 분석하여 추출한 것입니다.