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  • 1
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 70 (1994), S. 569-578 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract Many neurons at the sensory periphery receive periodic input, and their activity exhibits entrainment to this input in the form of a preferred phase for firing. This article describes a modeling study of neurons which skip a random number of cycles of the stimulus between firings over a large range of input intensities. This behavior was investigated using analog and digital simulations of the motion of a particle in a double-well with noise and sinusoidal forcing. Well residence-time distributions were found to exhibit the main features of the interspike interval histograms (ISIH) measured on real sensory neurons. The conditions under which it is useful to view neurons as simple bistable systems subject to noise are examined by identifying the features of the data which are expected to arise for such systems. This approach is complementary to previous studies of such data based, e.g., on non-homogeneous point processes. Apart from looking at models which form the backbone of excitable models, our work allows us to speculate on the role that stochastic resonance, which can arise in this context, may play in the transmission of sensory information.
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  • 2
    Electronic Resource
    Electronic Resource
    Springer
    Biological cybernetics 70 (1994), S. 569-578 
    ISSN: 1432-0770
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Computer Science , Physics
    Notes: Abstract. Many neurons at the sensory periphery receive periodic input, and their activity exhibits entrainment to this input in the form of a preferred phase for firing. This article describes a modeling study of neurons which skip a random number of cycles of the stimulus between firings over a large range of input intensities. This behavior was investigated using analog and digital simulations of the motion of a particle in a double-well with noise and sinusoidal forcing. Well residence-time dis tributions were found to exhibit the main features of the interspike interval histograms (ISIH) measured on real sensory neurons. The conditions under which it is useful to view neurons as simple bistable systems subject to noise are examined by identifying the features of the data which are expected to arise for such systems. This approach is complementary to previous studies of such data based, e.g., on nonhomogeneous point processes. Apart from looking at models which form the backbone of excitable model s, our work allows us to speculate on the role that stochastic resonance, which can arise in this context, may play in the transmission of sensory information.
    Type of Medium: Electronic Resource
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  • 3
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Nature 423, 77–81 (2003). In this Letter, we inadvertently omitted to give the species name, Apteronotus leptorhynchus (brown ghost knife-fish), of the weakly electric fish used in our ...
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  • 4
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Animals have developed stereotyped communication calls to which specific sensory neurons are well tuned. These communication calls must be discriminated from environmental signals such as those produced by prey. Sensory systems might have evolved neural circuitry to encode both categories. In ...
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  • 5
    ISSN: 1476-4687
    Source: Nature Archives 1869 - 2009
    Topics: Biology , Chemistry and Pharmacology , Medicine , Natural Sciences in General , Physics
    Notes: [Auszug] Stimulus-induced oscillations occur in visual, olfactory and somatosensory systems. Several experimental and theoretical studies have shown how such oscillations can be generated by inhibitory connections between neurons. But the effects of realistic spatiotemporal sensory input on oscillatory ...
    Type of Medium: Electronic Resource
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  • 6
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 5 (1995), S. 209-215 
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: Periodically driven nonlinear oscillators can exhibit a form of phase locking in which a well-defined feature of the motion occurs near a preferred phase of the stimulus, but a random number of stimulus cycles are skipped between its occurrences. This feature may be an action potential, or another crossing by a state variable of some specific value. This behavior can also occur when no apparent external periodic forcing is present. The phase preference is then measured with respect to a time scale internal to the system. Models of these behaviors are briefly reviewed, and new mechanisms are presented that involve the coupling of noise to the equations of motion. Our study investigates such stochastic phase locking near bifurcations commonly present in models of biological oscillators: (1) a supercritical and (2) a subcritical Hopf bifurcation, and, under autonomous conditions, near (3) a saddle-node bifurcation, and (4) chaotic behavior. Our results complement previous studies of aperiodic phase locking in which noise perturbs deterministic phase-locked motion. In our study however, we emphasize how noise can induce a stochastic phase-locked motion that does not have a similar deterministic counterpart. Although our study focuses on models of excitable and bursting neurons, our results are applicable to other oscillators, such as those discussed in the respiratory and cardiac literatures. © 1995 American Institute of Physics.
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  • 7
    Electronic Resource
    Electronic Resource
    Woodbury, NY : American Institute of Physics (AIP)
    Chaos 3 (1993), S. 167-176 
    ISSN: 1089-7682
    Source: AIP Digital Archive
    Topics: Physics
    Notes: The dependence of solution behavior to perturbations of the initial function (IF) in a class of nonlinear differential delay equations (DDEs) is investigated. The structure of basins of attraction of multistable limit cycles is investigated. These basins can possess complex structure at all scales measurable numerically although this is not necessarily the case. Sensitive dependence of the asymptotic solution to perturbations in the initial function is also observed experimentally using a task specific electronic analog computer designed to investigate the dynamics of an integrable first-order DDE.
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  • 8
    Electronic Resource
    Electronic Resource
    Springer
    Bulletin of mathematical biology 51 (1989), S. 605-624 
    ISSN: 1522-9602
    Source: Springer Online Journal Archives 1860-2000
    Topics: Biology , Mathematics
    Notes: Abstract Neurophysiological and anatomical observations are used to derive a non-linear delay-differential equation for the pupil light reflex with negative feedback. As the gain or the time delay in the reflex is increased, a supercritical Hopf bifurcation occurs from a stable fixed point to a stable limit cycle oscillation in pupil area. A Hopf bifurcation analysis is used to determine the conditions for instability and the period and amplitude of these oscillations. The more complex waveforms typical of the occurrence of higher order bifurcations were not seen in numerical simulations of the model. This model provides a general framework to study the different types of dynamical behaviors which can be produced by the pupil light reflex, e.g. edge-light pupil cycling.
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  • 9
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 60 (1990), S. 735-751 
    ISSN: 1572-9613
    Keywords: Stochastic differential equations ; Fokker-Planck equation ; Hopf bifurcation ; Liapunov functions ; global stability ; noise-induced transitions
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract We prove analytically that additive and parametric (multiplicative) Gaussian distributed white noise, interpreted in either the Itô or Stratonovich formalism, induces global asymptotic stability in two prototypical dynamical systems designated as supercritical (the Landau equation) and subcritical, respectively. In both systems without noise, variation of a parameter leads to a switching between a single, globally stable steady state and multiple, locally stable steady states. With additive noise this switching is mirrored in the behavior of the extrema of probability densities at the same value of the parameter. However, parametric noise causes a noise-amplitude-dependent shift (postponement) in the parameter value at which the switching occurs. It is shown analytically that the density converges to a Dirac delta function when the solution of the Fokker-Planck equation is no longer normalizable.
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  • 10
    Electronic Resource
    Electronic Resource
    Springer
    Journal of statistical physics 70 (1993), S. 309-327 
    ISSN: 1572-9613
    Keywords: Stochastic resonance ; neuron models
    Source: Springer Online Journal Archives 1860-2000
    Topics: Physics
    Notes: Abstract Periodically stimulated sensory neurons typically exhibit a kind of “statistical phase locking” to the stimulus: they tend to fire at a preferred phase of the stimulus cycle, but not at every cycle. Hence, the histogram of interspike intervals (ISIH), i.e., of times between successive firings, is multimodal for these neurons, with peaks centered at integer multiples of the driving period. A particular kind of residence time histogram for a large class of noisy bistable systems has recently been shown to exhibit the major features of the neural data. In the present paper, we show that an excitable cell model, the Fitzhugh-Nagumo equations, also reproduces these features when driven by additive periodic and stochastic forces. This model exhibits its own brand of stochastic resonance as the peaks of the ISIH successively go through a maximum when the noise intensity is increased. Further, the presence of a noise-induced limit cycle introduces a third time scale in the problem. This limit cycle is found to modify qualitatively the phase-locking picture, e.g., by suppressing certain peaks in the ISIH. Finally, the role of noise and possibly of stochastic resonance (SR) in the neural encoding of sensory information is discussed.
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