某些激励-抑制网络中物理测度的存在性
Existence of physical measures in some Excitation-Inhibition Networks
摘要：
在本文中，我们提出了一个严格的分析一类耦合的动力系统，其中两种不同类型的组件，一个兴奋和其他抑制，相互作用。这些网络模型的大小是有限的，但可以是任意大的。它们受到真实生物网络的启发，并具有生物系统中理想化的特征。网络的各个组成部分由简单的、研究较多的动力系统表示。网络层次上的复杂动态模式是其组成子系统之间耦合的结果。借助非均匀双曲理论中已有的方法，研究了它们的李雅普诺夫指数和熵，证明了大时间网络动力学是由具有SRB性质的物理测度所控制的.
英文摘要：
In this paper we present a rigorous analysis of a class of coupled dynamical systems in which two distinct types of components, one excitatory and the other inhibitory, interact with one another. These network models are finite in size but can be arbitrarily large. They are inspired by real biological networks, and possess features that are idealizations of those in biological systems. Individual components of the network are represented by simple, much studied dynamical systems. Complex dynamical patterns on the network level emerge as a result of the coupling among its constituent subsystems. Appealing to existing techniques in (nonuniform) hyperbolic theory, we study their Lyapunov exponents and entropy, and prove that large time network dynamics are governed by physical measures with the SRB property.
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