## 4 Results and Discussion
### Multi-Microwave Sources Collaborative Switching Heating  
A numerical simulation example in Section 4.1 demonstrates that the switching system has a specific resistance to DoS attacks. However, this performance improvement comes at the cost of sacrificing the system's consistency convergence ability and increasing uncertainty. As shown in Figure 3, the High Voltage DC Power Supply driver controls the magnetron, assuming that the power output of the magnetron is stable and without time delay, using the event-triggered switching model described in Equation (11) in Section 3.2, the intelligent agent in the multi-microwave sources controls the High Voltage DC Power Supply driver to activate the magnetrons. By optimizing the power output frequency in the leader's time domain, the follower can use control strategy Equation (11) to ensure a consistent switch between the high and low power of the magnetron. The multi-microwave sources intelligent system feeds the same total energy into the cavity at \(P_{1}=100\) w and t = 40 s. Eight experiments are conducted to compare different time-frequency distribution switching strategies by altering the leader state variables \(\psi\) and \(\zeta\). Control group (a) was heated with traditional constant power. Figure 8 displays that the total power utilized in all experiments is unchanged. The heating cycles of four groups (b-e) are fixed for 10 s, with corresponding \(P_{2}(t)/(P_{2}(t)+P_{1}(t))\) values of 0.8, 0.7, 0.6, and 0.5, respectively. Another four groups (f-i) have a fixed \(P_{2}(t)/(P_{2}(t)+P_{1}(t))\) value of 0.5, but the heating cycles are set at 20 s, 10 s, 8 s, and 5 s, respectively. \[|S_{11}|=\frac{i\int_{0}^{t}P(\tau)d(\tau)-\int_{0}^{t}\int_{\
u}Q_{\epsilon}( \tau)dVA_{\tau}}{i\int_{0}^{t}P(\tau)d(\tau)} \tag{24}\] \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Agent i** & **1** & **2** & **3** & **4** & **5** \\ \hline Exist DoS attacks & 118 & 116 & 112 & 105 & 106 \\ Absent DoS attacks (method of [25]) & 94 & 101 & 90 & 88 & 95 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: The number of event triggers is based on comparing the event and DoS attacks. Figure 7: Event-triggered time distribution of intelligent agents under DoS attacks. \[COV=\sqrt{\frac{\sqrt{\frac{\sum\limits_{k=1}^{n}{{{(T_{k}-\hat{T})}^{2}}}}}{{n( \hat{T}-T_{0})}^{2}}}} \tag{25}\]  
Using COMSOL software (version: COMSOL Multiphysics(r) 6.2) for finite element modeling and simulation experiments, the electromagnetic power loss density \(Q_{e}(\tau)\) of the material is recorded. In order to evaluate the heating effect of materials in the microwave, the ratio of reflected power to input power \(|S_{11}|\) and temperature variation coefficient \(COV\) are introduced [16; 25]. Where \(Q_{e}(\tau)\) and \(p(\tau)\) represent the electromagnetic power loss density and power value distribution in the time domain of the microwave source, respectively, \(n\) is the number of sampling points for material temperature, and the COMSOL built-in program selects the position and number of points used. \(T_{k}\) denotes the temperature value of sampling point \(k\), \(T_{0}\) is the initial temperature of the material, and \(\bar{T}\)denotes the average temperature of the sampling points. When the value of \(|S_{11}|\) is smaller, the utilization efficiency of microwave energy is higher. The temperature distribution of the material becomes more uniform as the value of \(COV\) decreases. Calculate the temperature difference between the highest and lowest temperatures after SiC heating using \(\delta T=T_{\max}-T_{\min}\); the variables \(T_{\max}\) and \(T_{\min}\) denote the highest and lowest temperatures, respectively. Table 4 describes the value of \(|S_{11}|\), \(COV\), and \(\delta T\) of SiC under different heating methods. Figure 8: Output power curve of multi-microwave sources under different switching strategies.