具有高阶相互作用的振子网络中的存储器选择和信息交换
Memory selection and information switching in oscillator networks with higher-order interactions
摘要：
我们研究了具有高阶相互作用的耦合振子网络的动力学及其存储信息的能力。特别是，这些振荡器系统的固定点由两个振荡器集群组成，它们以相反的相位被夹带，很容易映射到更常见的由0和1的序列表示的信息。虽然$2^N$这样的固定点状态存在于一个系统的$N$振荡器，我们发现，这些相对较小的一部分是稳定的，所选择的网络拓扑结构。为了理解这种振荡器网络的记忆选择，我们导出了一个稳定性准则来精确地识别哪些状态是稳定的，即，哪些信息片段由网络支持。我们还调查的过程中，系统可以在不同的稳定状态之间切换时，施加随机扰动，可能会迫使系统进入另一个稳定状态的吸引力盆。
英文摘要：
We study the dynamics of coupled oscillator networks with higher-order interactions and their ability to store information. In particular, the fixed points of these oscillator systems consist of two clusters of oscillators that become entrained at opposite phases, mapping easily to information more commonly represented by sequences of 0's and 1's. While $2^N$ such fixed point states exist in a system of $N$ oscillators, we find that a relatively small fraction of these are stable, as chosen by the network topology. To understand the memory selection of such oscillator networks, we derive a stability criterion to identify precisely which states are stable, i.e., which pieces of information are supported by the network. We also investigate the process by which the system can switch between different stable states when a random perturbation is applied that may force the system into the basin of attraction of another stable state.
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