Taming chaos: Stabilization of aperiodic attractors by noise
Taming chaos: Stabilization of aperiodic attractors by noise
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DOI：
10.1109/81.633888
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发表时间：
1997-10-01
期刊：
影响因子：
--
通讯作者：
Badler, J
中科院分区：
文献类型：
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作者：
Freeman, WJ;Chang, HJ;Badler, J
一个名为“KIII”的嗅觉系统模型包含64个模拟嗅球（OB）的耦合振荡器阵列，通过低通滤波线从模拟前嗅核（AON）和预状皮质（PC）的单个振荡器中获得负反馈和正反馈，它是用C语言实现的，可以在Macintosh， IBM或UNIX平台上运行，输出可以通过参数优化设置为点，极限环，准周期或非周期（可能是混沌的）吸引子。前三类解在参数变化和输入扰动下是稳定的，但它们在生物学上是不现实的。混沌解模拟了嗅觉动作电位和脑电图的时变密度特性，但在模拟运行时间的几秒钟后，它们就会过渡到点、极限环或准周期吸引子的盆地。尽管使用双精度算法给出64位字，但KIII模型对参数和输入终端位的变化非常敏感。随着OB中耦合振荡器数量的增加，全局稳定性降低，表明吸引子拥挤将模型中盆地的大小减小到数字化步骤的大小（类似于10(-16)），具有生物真实性的混沌解通过引入低水平，来自两个生物决定点的随机数发生器的加性噪声：每个受体输入线上的校正的空间非相干噪声，以及AON的空间相干噪声，AON是一个接收来自前脑各个部分的离心输入的全局控制点。提出了通过测量多个混沌输出来评估高维系统全局稳定性的方法，给出了KIII模型中连接权（增益）变化的稳定性范围，并设计了用于模式分类的系统。
A model named ''KIII'' of the olfactory system contains an array of 64 coupled oscillators simulating the olfactory bulb (OB), with negative and positive feedback through low-pass filter lines from single oscillators simulating the anterior olfactory nucleus (AON) and prepyriform cortex (PC), It is implemented in C to run on Macintosh, IBM, or UNIX platforms, The output can be set by parameter optimization to point, limit cycle, quasi-periodic, or aperiodic (presumably chaotic) attractors. The first three classes of solutions are stable under variations of parameters and perturbations by input, but they are biologically unrealistic. Chaotic solutions simulate the properties of time-dependent densities of olfactory action potentials and EEG's, but they transit into the basins of point, limit cycle, or quasiperiodic attractors after only a few seconds of simulated run time. Despite use of double precision arithmetic giving 64-bit words, the KIII model is exquisitely sensitive to changes in the terminal bit of parameters and inputs, The global stability decreases as the number of coupled oscillators in the OB is increased, indicating that attractor crowding reduces the size of basins in the model to the size of the digitizing step (similar to 10(-16)), Chaotic solutions having biological verisimilitude are robustly stabilized by introducing low-level, additive noise from a random number generator at two biologically determined points: rectified, spatially incoherent noise on each receptor input line, and spatially coherent noise to the AON, a global control point receiving centrifugal inputs from various parts of the forebrain. Methods are presented for evaluating global stability in the high dimensional system from measurements of multiple chaotic outputs, Ranges of stability are shown for variations of connection weights (gains) in the KIII model, The system is devised for pattern classification.