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  • 1
    Electronic Resource
    Electronic Resource
    Reduction of a channel-based model for a stomatogastric ganglion LP neuron (1993)
    Springer
    Biological cybernetics 69 (1993), S. 129-137 
    Details
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Buchholtz et al. constructed a detailed conductance-based model of the LP cell of the stomatogastric ganglion of crustacea based upon the experimental work of Golowasch. Their model incorporated seven ionic currents and had 13 dynamical variables. We have produced a simplification of this model that has a seven-dimensional phase space by using the method of equivalent potentials, suggested by Abbott and Kepler, to combine several dynamical variables with similar time scales. Analysis of the dynamics of the reference and reduced model reveals similar bifurcation diagrams and similar dynamical behavior of the individual ionic currents.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF00226196
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  • 2
    Electronic Resource
    Electronic Resource
    THE BIFURCATION OF QUADRATIC FUNCTIONS (1979)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 316 (1979), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1979.tb29459.x
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  • 3
    Electronic Resource
    Electronic Resource
    ONE-DIMENSIONAL DYNAMICS (1980)
    Oxford, UK : Blackwell Publishing Ltd
    Annals of the New York Academy of Sciences 357 (1980), S. 0 
    Details
    ISSN: 1749-6632
    Source: Blackwell Publishing Journal Backfiles 1879-2005
    Topics: Natural Sciences in General
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1111/j.1749-6632.1980.tb29701.x
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  • 4
    Electronic Resource
    Electronic Resource
    Noise in chaotic systems (1982)
    [s.l.] : Nature Publishing Group
    Nature 298 (1982), S. 358-361 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Consider a fluid experiment such as Rayleigh-Brnard convection or the flow between concentric cylinders in a regime which produces aperiodic flow3. Substantial theoretical and experimental attention has been given to the temporal characteristics of these flows as dynamical systems. The Landau-Hopf ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/298358a0
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  • 5
    Electronic Resource
    Electronic Resource
    Bifurcation, Bursting, and Spike Frequency Adaptation (1997)
    Springer
    Journal of computational neuroscience 4 (1997), S. 257-277 
    Details
    ISSN: 1573-6873
    Keywords: bifurcation ; bursting ; singular perturbation ; spike frequency adaptation ; stomatogastric ganglion
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract Many neural systems display adaptive properties that occur on timescales that are slower than the time scales associated withrepetitive firing of action potentials or bursting oscillations. Spike frequency adaptation is the name givento processes thatreduce the frequency of rhythmic tonic firing of action potentials,sometimes leading to the termination of spiking and the cell becomingquiescent. This article examines these processes mathematically,within the context of singularly perturbed dynamical systems.We place emphasis on the lengths of successive interspikeintervals during adaptation. Two different bifurcation mechanisms insingularly perturbed systems that correspond to the termination offiring are distinguished by the rate at which interspike intervalsslow near the termination of firing. We compare theoreticalpredictions to measurement of spike frequency adaptation in a modelof the LP cell of the lobster stomatogastric ganglion.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008871803040
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  • 6
    Electronic Resource
    Electronic Resource
    An Improved Parameter Estimation Method for Hodgkin-Huxley Models (1999)
    Springer
    Journal of computational neuroscience 6 (1999), S. 145-168 
    Details
    ISSN: 1573-6873
    Keywords: Hodgkin-Huxley models ; parameter estimation ; voltage clamp ; least squares
    Source: Springer Online Journal Archives 1860-2000
    Topics: Computer Science , Medicine , Physics
    Notes: Abstract We consider whole-cell voltage-clamp data of isolated currents characterized by the Hodgkin-Huxley paradigm. We examine the errors associated with the typical parameter estimation method for these data and show them to be unsatisfactorally large especially if the time constants of activation and inactivation are not sufficiently separated. The size of these errors is due to the fact that the steady-state and kinetic properties of the current are estimated disjointly. We present an improved parameter estimation method that utilizes all of the information in the voltage-clamp conductance data to estimate steady-state and kinetic properties simultaneously and illustrate its success compared to the standard method using simulated data and data from P. interruptus shal channels expressed in oocytes.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1023/A:1008880518515
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  • 7
    Electronic Resource
    Electronic Resource
    An arresting phenomenon (1987)
    [s.l.] : Nature Publishing Group
    Nature 328 (1987), S. 211-212 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] PHASE is incompatible with time. This statement is an interpretation of the basic topological fact that there is no way of defining a continuous, increasing function on a circle. Arthur Winfree has devoted his career to exploring the biological con-sequences of this theorem and analogous ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/328211a0
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  • 8
    Electronic Resource
    Electronic Resource
    Dynamic model (1989)
    [s.l.] : Nature Publishing Group
    Nature 341 (1989), S. 368-368 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Nonlfnearlty. Honorary editors J.D. Gibbon and D.A. Rand. Institute of Physics and London Mathematical Society. 4/yr. UK £178, North America $338. In the United States distributed by the American Institute of Physics. THE joint sponsorship of Nonlinearity (by the London Mathematical ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/341368a0
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  • 9
    Electronic Resource
    Electronic Resource
    In support of catastrophe theory (1977)
    [s.l.] : Nature Publishing Group
    Nature 270 (1977), S. 383-384 
    Details
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] SIR,-While I do not wish to perpetuate unwarranted enthusiasm for the ability of catastrophe theory to transform the natural and social sciences, I believe that Zahler and Sussmann (27 October, page 759) have overstepped the bounds of decency in their vehement attack. Let me point out a few ...
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1038/270383a0
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  • 10
    Electronic Resource
    Electronic Resource
    Limit sets ofS-unimodal maps with zero entropy (1987)
    Springer
    Communications in mathematical physics 110 (1987), S. 655-659 
    Details
    ISSN: 1432-0916
    Source: Springer Online Journal Archives 1860-2000
    Topics: Mathematics , Physics
    Notes: Abstract One-dimensional mappings “at the limit of period doubling” are studied in this paper without the use of the renormalization theory of Feigenbaum and others. The principal result is that the attracting part of the nonwandering set is a Cantor set of measure zero under the additional assumption that the map has negative Schwarzian derivative.
    Type of Medium: Electronic Resource
    URL: http://dx.doi.org/10.1007/BF01205554
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