论文标题
在神经网络动力学的分支模型中通往混乱的途径
Route to chaos in a branching model of neural network dynamics
论文作者
论文摘要
简化的模型是理解集体神经网络动态的必要垫脚石，特别是不同种类的行为之间的过渡，这些行为可以通过这种模型捕获，而不会偏见。一种这样的模型，即皮质分支模型（CBM），以前已被用来表征神经网络动力学的普遍行为的一部分，并导致发现了第二个混乱的过渡，但尚未充分表征。在这里，我们研究了这种混乱的过渡的特性，该特性发生在$ k _ {\ sf in} = 1 $ cbm中的平均场近似值中，该模型将模型施加在lyapunov spect上的初始条件，参数及其烙印上。尽管该模型似乎与Hénon图相似，但我们发现无法使用正交转换来恢复Hénon图来使动力学解析。两者之间的根本差异，即CBM在紧凑的空间上定义并具有非恒定的雅各布式，这表明CBM地图（更广泛地说）代表了一类广义Hénon地图，尚未完全理解。
Simplified models are a necessary steppingstone for understanding collective neural network dynamics, in particular the transitions between different kinds of behavior, whose universality can be captured by such models, without prejudice. One such model, the cortical branching model (CBM), has previously been used to characterize part of the universal behavior of neural network dynamics and also led to the discovery of a second, chaotic transition which has not yet been fully characterized. Here, we study the properties of this chaotic transition, that occurs in the mean-field approximation to the $k_{\sf in}=1$ CBM by focusing on the constraints the model imposes on initial conditions, parameters, and the imprint thereof on the Lyapunov spectrum. Although the model seems similar to the Hénon map, we find that the Hénon map cannot be recovered using orthogonal transformations to decouple the dynamics. Fundamental differences between the two, namely that the CBM is defined on a compact space and features a non-constant Jacobian, indicate that the CBM maps, more generally, represent a class of generalized Hénon maps which has yet to be fully understood.
