División de Matemáticas Aplicadas, Instituto Potosino de Investigación Científica y Tecnológica A. C., Camino a la Presa San José 2055, Col. Lomas 4 Sección, C.P. 78216, San Luis Potosí, S.L.P., Mexico.
Facultad de Ciencias, Universidad Autónoma de San Luis Potosí, Álvaro Obregón 64, C.P. 78000, San Luis Potosí, S.L.P., Mexico.
Chaos. 2015 Aug;25(8):083113. doi: 10.1063/1.4928739.
We present the design of an autonomous time-delay Boolean network realized with readily available electronic components. Through simulations and experiments that account for the detailed nonlinear response of each circuit element, we demonstrate that a network with five Boolean nodes displays complex behavior. Furthermore, we show that the dynamics of two identical networks display near-instantaneous synchronization to a periodic state when forced by a common periodic Boolean signal. A theoretical analysis of the network reveals the conditions under which complex behavior is expected in an individual network and the occurrence of synchronization in the forced networks. This research will enable future experiments on autonomous time-delay networks using readily available electronic components with dynamics on a slow enough time-scale so that inexpensive data collection systems can faithfully record the dynamics.
我们提出了一种使用现成电子元件实现的自主时滞布尔网络的设计。通过模拟和实验，考虑到每个电路元件的详细非线性响应，我们证明了具有五个布尔节点的网络可以显示复杂的行为。此外，我们还表明，当受到共同的周期性布尔信号的强制时，两个相同网络的动力学可以迅速同步到周期性状态。对网络的理论分析揭示了在单个网络中预期出现复杂行为的条件，以及在强制网络中发生同步的条件。这项研究将使未来能够使用动态足够慢的现成电子元件进行自主时滞网络的实验，以便使用廉价的数据采集系统忠实地记录动力学。
