## 1 Introduction  
Wireless sensor networks (WSNs) have recently received increased attention for a broad array of applications such as surveillance, environment monitoring, medical diagnostics, and industrial control. A WSN typically includes many inexpensive wireless sensor nodes, each of which can collect, process, and store environmental information. Nodes in WSNs generally rely on portable power sources, such as batteries, to provide the necessary power. Power management of WSNs is critical. Numerous protocols have been proposed to extend the lifetime of sensor networks in their optimizing deployment methods [1,2]. For wakeup mechanisms of pending transmissions, the major objective is to maintain network connectivity when reducing idle-state energy consumption. Existing wakeup mechanisms include three approaches: on-demand wakeup, scheduled rendezvous wakeup, and asynchronous wakeup. In an on-demand wakeup approach, when nodes receive out-of-band signals, which are used to help the signals or nodes stay on the paging channel, it means that these sleeping nodes wake up in an on-demand manner. However, despite the efficiency of this strategy, complexity and network size dependability are drawbacks [3]. In the scheduled rendezvous wakeup mechanism, system controllers schedule the same wakeup time periodically to communicate with low-power sleeping nodes, such as S-Mac or multi-parent scheme protocols [4]. This mechanism is used in IEEE 802.11 and Bluetooth, and all the involved nodes must synchronize their clocks according to the common wakeup time schedule, in order to exchange their data in time. The drawbacks of this approach are system confirmation and clock synchronization. The final approach is asynchronous wakeup, in contrast to the scheduled rendezvous wakeup approach, which requires no clock synchronization. In other words, each node follows its own wakeup schedule in the idle state and communicates with other overlapping neighbors. To meet this requirement, nodes in this mechanism generally must wake up more frequently compared with scheduled rendezvous mechanisms. Asynchronous wakeup is easier to implement and can maintain network connections even in a highly dynamic situation. However, energy consumption and the robustness of network connectivity trade off in asynchronous wakeup mechanisms [5,6]. Most existing solutions to these types of problems entail using pattern wakeup schedules to satisfy the following requirements:  
1. Discovering the neighbor in a reasonable time frame;
2. Minimizing the time slots in the node's wakeup time;
3. Matching the nodes awake-sleep schedules within their heterogeneous battery duty cycle. These solutions can be categorized into quorum-based and co-primality based protocols. Quorum-based protocols select wakeup times according to the quorums arranged by the radios' time slots and add them into the matrix. The row and column arrangements are based on the protocol scheme, which typically assigns active or sleeping slots. Active time slots then overlap with the active time slots of neighboring nodes. When two nodes have the same duty cycle, they can meet each other during the active times from the row and column in the matrix regardless of clock drifts [7]. In addition, co-primality based protocols exploit Chinese Remainder Theorem properties to ensure the same active times in the same slots between two nodes [8]. According to these protocols, nodes wake up at specific time slots multiplied by the protocol parameters, and these numbers are coprime to one another. Thus,nodes can discover one another within a bounded time and delay [9]. In [10], the authors consider the characteristics of sensor network environment, and proposed the mechanism to create exchange keys on the derivation of a one-time password in a two-dimensional quorum system. This study focused on the development of a dynamic quorum system, which attempts to archive efficient neighbor discovery and rendezvous maintenance.