Closed-loop stabilization of the Jamming Avoidance Response reveals its locally unstable and globally nonlinear dynamics
Closed-loop stabilization of the Jamming Avoidance Response reveals its locally unstable and globally nonlinear dynamics
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DOI：
10.1242/jeb.088922
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发表时间：
2013-11-01
影响因子：
2.8
通讯作者：
Cowan, Noah J.
中科院分区：
文献类型：
--
作者：
Madhav, Manu S.;Stamper, Sarah A.;Cowan, Noah J.
弱电鱼类的干扰回避反应，或JAR，已经在所有组织水平上进行了分析，从整个有机体的行为到特定的离子通道。然而，根据动态系统模型对JAR行为的简明描述还没有实现，至少部分原因是由于“回避”行为本质上是不稳定的和非线性的。我们通过关闭围绕动物行为反应的反馈回路，克服了绿色特征曼尼亚中罐子的不稳定性。具体地说，干扰刺激的瞬时频率通过反馈法则与鱼自己的产生电的频率联系在一起。如果没有反馈，鱼自身的频率会偏离刺激频率，但适当的反馈会稳定行为。在稳定系统后，我们测量了鱼对各种刺激的瞬时频率反应。时滞一阶线性系统模型符合平衡点附近的行为。白噪声刺激的一致性以及不同刺激类型之间的数量一致性支持这一局部线性模型。接下来，我们使用钳位频差实验来检查行为的内在非线性，以将模型扩展到平衡邻域之外。由此产生的非线性模型由相互竞争的运动返回项和感觉逃逸项组成。该模型再现了差频(Df)中阶跃和斜坡变化的响应，并预测了作为差频的函数的“跳跃”分叉，这一点我们在实验上得到了证实。
The Jamming Avoidance Response, or JAR, in the weakly electric fish has been analyzed at all levels of organization, from whole-organism behavior down to specific ion channels. Nevertheless, a parsimonious description of the JAR behavior in terms of a dynamical system model has not been achieved at least in part due to the fact that 'avoidance' behaviors are both intrinsically unstable and nonlinear. We overcame the instability of the JAR in Eigenmannia virescens by closing a feedback loop around the behavioral response of the animal. Specifically, the instantaneous frequency of a jamming stimulus was tied to the fish's own electrogenic frequency by a feedback law. Without feedback, the fish's own frequency diverges from the stimulus frequency, but appropriate feedback stabilizes the behavior. After stabilizing the system, we measured the responses in the fish's instantaneous frequency to various stimuli. A delayed first-order linear system model fitted the behavior near the equilibrium. Coherence to white noise stimuli together with quantitative agreement across stimulus types supported this local linear model. Next, we examined the intrinsic nonlinearity of the behavior using clamped frequency difference experiments to extend the model beyond the neighborhood of the equilibrium. The resulting nonlinear model is composed of competing motor return and sensory escape terms. The model reproduces responses to step and ramp changes in the difference frequency (df) and predicts a 'snap-through' bifurcation as a function of dF that we confirmed experimentally.