Edge computing brings computation and storage resources to the edge of the mobile network to solve the problems of low latency and high real-time demand. However, edge computing is more vulnerable to malicious attacks due to its open and dynamic environments. In this article, we investigate security defense strategies in edge computing systems, focusing on scenarios with one attacker and multiple defenders to determine optimal defense strategies with minimal resource allocation. Firstly, we formulate the interactions between the defenders and the attackers as the mean-field Stackelberg game model, where the state and the objective functions of the defenders are coupled through the mean-field term, and are strongly influenced by the strategy of the attacker. Then, we analyze the local optimal strategies of the defenders given an arbitrary strategy of the attackers. We demonstrate the Nash equilibrium and the mean-field equilibrium for both the defenders and the attackers. Finally, simulation analysis will illustrate the dynamic evolution of the defense strategy of the defenders and the trajectory of the attackers based on the proposed Stackelberg game model.

The dynamic changes of mobile terminals have led to the more complex environment for edge computing resource allocation. Edge nodes are generally mobile wireless devices or network devices with limited processing capacity, and have relatively limited computing resources. The importance of computing tasks for terminal devices changes dynamically , and the corresponding computing efficiency also changes. Therefore , the dynamic resource allocation is particularly important in the edge computing environments. In order to maximize the efficiency of using edge computing resources, increase the profit of edge node, and reduce the cost of edge terminal devices, exploring an efficient dynamic resource pricing and allocation mechanism for edge computing is an urgent problem that we need to solve. In this paper, 1 Springer Nature 2021 L A T E X template Dynamic Pricing in Edge computing Resource Allocation Based on Stackelberg Dynam we describe the dynamic pricing and resource allocation problem between edge node and terminal devices as a Stackelberg dynamic game model, and solve the Nash equilibrium solution of the model through Bellman dynamic programming theory. During the resource allocation process, to get the optimal computing resource price of edge node and the optimal computing resource usage of terminal devices.

To address the challenge of imprecise detection and control of fertilizer application rates caused by high granular flow during fertilization operations, a parallel diversion detection method with real-time application rate regulation is proposed. The mechanism of uniform distribution of discrete particles formed by high-throughput aggregated granular fertilizer was elucidated. Key components including the uniform fertilizer tube, sensor detection structure, six-channel diversion cone disc, and fertilizer convergence tube underwent parametric design, culminating in the innovative development of a six-channel parallel diversion detection device. A multi-channel parallel signal detection method was studied, and a synchronous multi-channel signal acquisition system was designed. Through calibration tests, relationship models were established between the measured flow rate of granular fertilizer and voltage, as well as between the actual flow rate and the rotational speed of the fertilizer discharge shaft. A fuzzy PID control model was constructed in MATLAB2023/Simulink. Using overshoot, response time, and stability as evaluation metrics, the control performance of traditional PID and fuzzy PID was compared and analyzed. To validate the control system’s precision, device performance tests were conducted. Results demonstrated that fuzzy PID control reduced the time required to reach steady state by 66.87% compared to traditional PID, while overshoot decreased from 7.38 g·s⁻¹ to 1.49 g·s⁻¹. Divergence uniformity tests revealed that at particle generation rates of 10, 20, 30, and 40 g·s⁻¹, the coefficient of variation for channel divergence consistency gradually increased with rising tilt angles. During field operations at 0–5.0° tilt, the coefficient of variation for channel divergence consistency remained below 7.72%. Bench tests revealed that the fuzzy PID control system achieved an average accuracy improvement of 3.64% compared to traditional PID control, with a maximum response time of 0.9 s. Field trials demonstrated detection accuracy no less than 92.64% at normal field operation speeds of 3.0–6.0 km·h⁻¹. This system enables real-time, precise detection of fertilizer application rates and closed-loop regulation.