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Nonlinear behaviour in a composite with a periodic microstructure

We discuss the nonlinear behaviour of a current in the two-dimensional periodic textures near the percolation metal-insulator transition. It is shown that the effective nonlinear conductivity and the fourth current and field correlation functions are anomalously great at finite values of the ratio of the linear conductivities of the cells, and the critical nonlinear properties of nonlinear textures depend on the microgeometry of the systems. A possibility of experimental investigation of predicted effects and a possibility to create nonlinear media is discussed.