We propose an adaptive master-slave coupling scheme to achieve explosive synchronization (ES) in a targeted (slave) layer of a multilayer network of Sakaguchi-Kuramoto (SK) oscillators. The natural frequencies of the oscillators in the networks are drawn from Lorentzian distribution of zero mean. In the absence of inter-layer coupling, the dynamics of the master layer is governed by SK model with local adaptive coupling and the layer exhibits ES for wide ranges of the parameters. On the other hand, the targeted layer also consists of SK model but does not exhibit ES. Under the proposed coupling scheme, a feedback is sent to a percentage of nodes in the slave layer in the form of local order parameters of the master layer to achieve ES in the slave layer. Our numerical experiment shows that the proposed coupling scheme can induce ES in the slave layer even when a very small percentage of nodes receive feedback from the master layer. The area of the hysteresis region in the slaved layer is found to be steadily increasing with the increase in the percentage of feedback receiving nodes of the slave layer. In the ES regime, an amplification in the hysteresis width in the slave layer is also achieved by tuning a parameter in the adaptive coupling function of the master layer. The scheme proposed here is found to be robust and can induce ES in a variety of networks in the slave layer.

我们提出了一种自适应的主从耦合方案，以在坂口-仓本（SK）振荡器的多层网络的目标（从）层中实现爆炸同步（ES）。网络中振荡器的固有频率来自零均值的洛伦兹分布。在不存在层间耦合的情况下，主控层的动力学由具有局部自适应耦合的SK模型控制，并且该层对于较大范围的参数均显示ES。另一方面，目标层也包含SK模型，但不显示ES。在提出的耦合方案下，以主层的本地顺序参数的形式向从属层中一定百分比的节点发送反馈，以在从属层中实现ES。我们的数值实验表明，即使很小比例的节点接收到来自主层的反馈，所提出的耦合方案也可以在从属层中诱发ES。发现随着从属层的反馈接收节点的百分比的增加，从属层中的磁滞区域的面积稳定地增加。在ES机制中，通过调整主层的自适应耦合功能中的参数，也可以实现从属层中磁滞宽度的放大。发现这里提出的方案是健壮的并且可以在从属层的各种网络中诱发ES。发现随着从属层的反馈接收节点的百分比的增加，从属层中的磁滞区域的面积稳定地增加。在ES机制中，通过调整主层的自适应耦合功能中的参数，也可以实现从属层中磁滞宽度的放大。发现这里提出的方案是健壮的并且可以在从属层的各种网络中诱发ES。发现随着从属层的反馈接收节点的百分比的增加，从属层中的磁滞区域的面积稳定地增加。在ES机制中，通过调整主层的自适应耦合功能中的参数，也可以实现从属层中磁滞宽度的放大。发现这里提出的方案是健壮的并且可以在从属层的各种网络中诱发ES。