Gassel Martin, Glatt Erik, Kaiser Friedemann
Institute of Applied Physics, Darmstadt University of Technology, Hochschulstrasse 4a, 64289 Darmstadt, Germany.
Phys Rev E Stat Nonlin Soft Matter Phys. 2008 Jun;77(6 Pt 2):066220. doi: 10.1103/PhysRevE.77.066220. Epub 2008 Jun 27.
The influence of time-delayed feedback on pattern formation in subexcitable media represented by a net of FitzHugh-Nagumo elements, a minimal model of neuronal dynamics, is studied. Without feedback, wave fronts die out after a short propagation length (subexcitable net dynamics). Applying time-delayed feedback with appropriate feedback parameters, pattern formation is sustained and the wave fronts may propagate through the whole net (signature of excitable behavior). The coherence of noise-induced patterns is significantly enhanced if feedback with appropriately chosen parameters is applied, and shows a resonancelike dependency on the delay time. In a next step, the transition to the excitable regime is investigated in dependence on the quota of elements, which get the feedback signal. It is sufficient to control approximately half of the elements to achieve excitable behavior. Regarding a medical application, where the external control of a neural tissue would affect not single neurons but clusters of neurons, the spatial correlation of the controlled elements is of importance. The selection of the elements, which get the feedback signal, is based on a spatially correlated random distribution. It is shown that the correlation length of this distribution affects the pattern formation.
研究了由FitzHugh-Nagumo元件网络（一种神经元动力学的最小模型）所代表的亚兴奋介质中，延迟反馈对模式形成的影响。在没有反馈的情况下，波前在短传播长度后就会消失（亚兴奋网络动力学）。应用具有适当反馈参数的延迟反馈，模式形成得以维持，波前可能会传播通过整个网络（兴奋性行为的特征）。如果应用具有适当选定参数的反馈，噪声诱导模式的相干性会显著增强，并表现出对延迟时间的类似共振的依赖性。接下来，根据接收反馈信号的元件配额，研究向兴奋状态的转变。控制大约一半的元件就足以实现兴奋性行为。对于医学应用而言，神经组织的外部控制会影响的不是单个神经元而是神经元簇，因此被控制元件的空间相关性很重要。接收反馈信号的元件的选择基于空间相关的随机分布。结果表明，这种分布的相关长度会影响模式形成。
