Research On Percolation And Robustness Of Electronic Information Network Under Complex Electromagnetic Environment

The complex electromagnetic environment is the complex form of the battlefield electromagnetic environment in space, time, frequency and energy domain. It has the following characteristics: wide space distribution, random time distribution, overlapped frequencies and uneven energy distribution. In information age, complex electromagnetic environment has a serious impact on the electronic information system, being the "nonlinear superposition effect" of the electronic information system simultaneously affected by various electromagnetic environment elements as well as ’’nonlinear transfer effect" of the information link in the electronic information system influenced by electromagnetic environment elements.In this dissertation, the electronic information system under the complex electromagnetic environment is regarded as a complex system and abstracted as a complex network by using the methods of network science. Based on the method used in the percolation theory of random graph, we study the percolation and robustness of the electronic information network under the complex electromagnetic environment. The main contents of this dissertation are as follows:1. By abstracting the "nonlinear superposition effect" of the electronic information system affected by complex electromagnetic environment as the adding-edges rule, we study the percolation behavior of random networks under a piecewise linear weighted function with a parameter ?. When tuning the value of ? from 1 to 0, the percolation transition can change from continuous to multiple discontinuous and strongly discontinuous. At ?=1, the percolation model is the classical Erd?s–Rényi(ER) random graph model, which has a continuous transition at the critical point 0.5. When ?=0, it is nearly at the final step of the adding-edges process that two clusters with linear size merge, inducing the largest gap of the order parameter and indicating a strongly discontinuous transition. When ? is not equal to 0 or 1, it is found that only merging the clusters with sizes no smaller than N?(N is the system size) can lead to a decline in the normalied occupation probability pr(L) of the clusters with sizes(?N?). At ?=1/3, there are much oscillation in the tail of the evolving pr(L), indicating a multiple discontinuous transition. Finally, the numerical simulations investigate the characteristics of the duration of the different order parameter in the three typical percolation transition processes.2. By abstracting the "nonlinear superposition effect" of the electronic information system affected by complex electromagnetic environment as the adding-edges rules, we study the percolation behaviors of random networks under a nonlinear weighted function, as well as the percolation behaviors of static and growing networks under a power function. For the network percolation behaviors of the nonlinear weighted function with a parameter ?, the percolation process at ?=1/N generates a continuous transition at the critical point 0.5, which is similar to the ER random graph model. At ?=1, the percolation process exhibits a strongly discontinuous transition at the critical point 1. When ?=N-1/2, the percolation process undergoes a multiple discontinuous transition. For the percolation behaviors of static network under the power function with a parameter ?, the percolation transition can switch from continuous to strongly discontinuous as the value of ? is tuned, which indicates that the percolation process exists a tricritical point ?0, and that the percolation transition is strongly discontinuous(?<?0) or continuous(?>?0). Finite scaling analysis shows that ?0=0, and that the percolation process at ?0=0 generates a strongly discontinuous transition. Compared with the weakly discontinuous transition in the static network, the growing network leads to a smoother continuous transition. While for the strongly discontinuous transition in the static network, the nature of strongly discontinuous transition remains unchanged in the growing network.3. By abstracting the "nonlinear superposition effect" of the electronic information system affected by various electromagnetic environment elements as the adding-edges rules, we study the percolation behaviors of random networks under hybrid rules and two-stage rules. In the random network percolation model under hybrid ER rule and min-cluster rule, with probability q the occupied edge at every time step is added according to the ER rule. With the decrease of the value of q, the percolation transition can change from continuous to strongly discontinuous, which indicates that the percolation process has a tricritical point qc. Based on the final vanishing moment of the each existing cluster in the percolation process, the numerical simulations estimate the tricritical point qc, being between 0.2<qc<0.25. Considering that many real world networks begin to evolve according to a certain rule from N isolated nodes, the intervention time point where another rule replaces the rule of the first stage is random. By denoting the intervention time point as a parameter, we study the percolation properties of the random networks under ER rule intervened by PR rule as well as PR rule intervened by ER rule.4. By abstracting the ’’nonlinear transfer effect" of the information link in the electronic information system influenced by complex electromagnetic environment as the cascading failure model in interdependent networks in which two networks generally has inter-similarity, we study how the inter-similarity degree affects the percolation behaviors. It is shown that as the value of the inter-similarity degree is larger the system is more robust. Considering that many interdependent networks are not randomly interdependent, we further investigate how nonrandom dependencies affect the percolation behaviors of interdependent networks with identical structure. It is indicated that when the dependencies are established between the nodes with approximate(considerably different) values of degrees, the interdependent networks become more robust(fragile).