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61.
Nonlinear dynamics provides a complementary framework to control theory for the quantitative analysis of the oculomotor control
system. This paper presents a number of findings relating to the aetiology and mechanics of the pathological ocular oscillation
jerk congenital nystagmus (jerk CN). A range of time series analysis techniques were applied to recorded jerk CN waveforms,
and also to simulated jerk waveforms produced by an established model in which the oscillations are a consequence of an unstable
neural integrator. The results of the analysis were then interpreted within the framework of a generalised model of the unforced
oculomotor system.
This work suggests that for jerk oscillations, the origin of the instability lies in one of the five oculomotor subsystems,
rather than in the final common pathway (the neural integrator and muscle plant). Additionally, experimental estimates of
the linearised foveation dynamics imply that a refixating fast phase induced by a near-homoclinic trajectory will result in
periodic oscillations. Local dimension calculations show that the dimension of the experimental jerk CN data increases during
the fast phase, indicating that the oscillations are not periodic, and hence that the refixation mechanism is of greater complexity
than a homoclinic reinjection. The dimension increase is hypothesised to result either from a signal-dependent noise process
in the saccadic system, or the activation of additional oculomotor components at the beginning of the fast phase. The modification
of a recent saccadic system model to incorporate biologically realistic signal-dependent noise is suggested, in order to test
the first of these hypotheses.
Action Editor: Peter Latham 相似文献
62.
The dynamics of the Hindmarsh-Rose (HR) model of bursting thalamic neurons is reduced to a system of two linear differential equations that retains the subthreshold resonance properties of the HR model. Introducing a reset mechanism after a threshold crossing, we turn this system into a resonant integrate-and-fire (RIF) model. Using Monte-Carlo simulations and mathematical analysis, we examine the effects of noise and the subthreshold dynamic properties of the RIF model on the occurrence of coherence resonance (CR). Synchronized burst firing occurs in a network of such model neurons with excitatory pulse-coupling. The coherence level of the network oscillations shows a stochastic resonance-like dependence on the noise level. Stochastic analysis of the equations shows that the slow recovery from the spike-induced inhibition is crucial in determining the frequencies of the CR and the subthreshold resonance in the original HR model. In this particular type of CR, the oscillation frequency strongly depends on the intrinsic time scales but changes little with the noise intensity. We give analytical quantities to describe this CR mechanism and illustrate its influence on the emerging network oscillations. We discuss the profound physiological roles this kind of CR may have in information processing in neurons possessing a subthreshold resonant frequency and in generating synchronized network oscillations with a frequency that is determined by intrinsic properties of the neurons.
PACS 05.45.-a, 05.40.Ca, 87.18.Sn, 87.19 相似文献
63.
Sacconi L Tolic-Nørrelykke IM D'Amico M Vanzi F Olivotto M Antolini R Pavone FS 《Cell biochemistry and biophysics》2006,45(3):289-302
Advances in the technologies for labeling and imaging biological samples drive a constant progress in our capability of studying
structures and their dynamics within cells and tissues. In the last decade, the development of numerous nonlinear optical
microscopies has led to a new prospective both in basic research and in the potential development of very powerful noninvasive
diagnostic tools. These techniques offer large advantages over conventional linear microscopy with regard to penetration depth,
spatial resolution, three-dimensional optical sectioning, and lower photobleaching. Additionally, some of these techniques
offer the opportunity for optically probing biological functions directly in living cells, as highlighted, for example, by
the application of second-harmonic generation to the optical measurement of electrical potential and activity in excitable
cells. In parallel with imaging techniques, nonlinear microscopy has been developed into a new area for the selective disruption
and manipulation of intracellular structures, providing an extremely useful tool of investigation in cell biology. In this
review we present some basic features of nonlinear microscopy with regard both to imaging and manipulation, and show some
examples to illustrate the advantages offered by these novel methodologies. 相似文献
64.
Many stage-structured density dependent populations with a continuum of stages can be naturally modeled using nonlinear integral projection models. In this paper, we study a trichotomy of global stability result for a class of density dependent systems which include a Platte thistle model. Specifically, we identify those systems parameters for which zero is globally asymptotically stable, parameters for which there is a positive asymptotically stable equilibrium, and parameters for which there is no asymptotically stable equilibrium. 相似文献
65.
Moira L. Steyn-Ross D. Alistair Steyn-Ross Jamie W. Sleigh 《Cognitive neurodynamics》2012,6(3):215-225
During slow-wave sleep, general anesthesia, and generalized seizures, there is an absence of consciousness. These states are
characterized by low-frequency large-amplitude traveling waves in scalp electroencephalogram. Therefore the oscillatory state
might be an indication of failure to form coherent neuronal assemblies necessary for consciousness. A generalized seizure
event is a pathological brain state that is the clearest manifestation of waves of synchronized neuronal activity. Since gap
junctions provide a direct electrical connection between adjoining neurons, thus enhancing synchronous behavior, reducing
gap-junction conductance should suppress seizures; however there is no clear experimental evidence for this. Here we report
theoretical predictions for a physiologically-based cortical model that describes the general anesthetic phase transition
from consciousness to coma, and includes both chemical synaptic and direct electrotonic synapses. The model dynamics exhibits
both Hopf (temporal) and Turing (spatial) instabilities; the Hopf instability corresponds to the slow (≲8 Hz) oscillatory
states similar to those seen in slow-wave sleep, general anesthesia, and seizures. We argue that a delicately balanced interplay
between Hopf and Turing modes provides a canonical mechanism for the default non-cognitive rest state of the brain. We show
that the Turing mode, set by gap-junction diffusion, is generally protective against entering oscillatory modes; and that
weakening the Turing mode by reducing gap conduction can release an uncontrolled Hopf oscillation and hence an increased propensity
for seizure and simultaneously an increased sensitivity to GABAergic anesthesia. 相似文献
66.
针对模拟大脑节律现象的Wilson-Cowan双节点耦合振子模型,选取满足该模型产生极限环振荡条件的参数,采用连续灰度阶图像块作为输入,兴奋性亚群节点响应作为图像增强的输出,做出刺激响应曲线,发现该曲线与图像处理领域中用于图像增强的Gamma校正曲线相似,说明Wilson-Cowan双节点耦合振子模型可以作为一种新的图像增强方法,同时也为基于Gamma校正曲线的图像增强提供了一种神经机制。将新方法与Retinex算法做对比,表现出了更好的图像增强性能。 相似文献
67.
68.
69.
We generalize to n patches the Ross-Macdonald model which describes the dynamics of malaria. We incorporate in our model the fact that some patches can be vector free. We assume that the hosts can migrate between patches, but not the vectors. The susceptible and infectious individuals have the same dispersal rate. We compute the basic reproduction ratio R(0). We prove that if R(0)1, then the disease-free equilibrium is globally asymptotically stable. When R(0)>1, we prove that there exists a unique endemic equilibrium, which is globally asymptotically stable on the biological domain minus the disease-free equilibrium. 相似文献
70.
Stengel RF 《Mathematical biosciences》2008,213(2):93-102
We examine the dynamics of infection by the human immunodeficiency virus (HIV), as well as therapies that minimize viral load, restore adaptive immunity, and use minimal dosage of anti-HIV drugs. Virtual therapies for wild-type infections are demonstrated; however, the HIV infection is never cured, requiring continued treatment to keep the condition in remission. With high viral turnover and mutation rates, drug-resistant strains of HIV evolve quickly. The ability of optimal therapy to contain drug-resistant strains is shown to depend upon the relative fitness of mutant strains. 相似文献