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This paper is devoted to energy-to-peak synchronization for uncertain reaction-diffusion delayed neural networks subject to external disturbances. The purpose is to determine a controller in such a way that the drive-response systems not only achieve asymptotical synchronization in the absence of disturbances but also possess a predefined energy-to-peak disturbance-rejection level under zero initial conditions. Through the use of Lyapunov-Krasovskii functionals and various integral inequalities, both delay-independent and dependent conditions are proposed in the form of linear matrix inequalities. When these conditions hold, the needed controller gains can be calculated directly. A numerical example is provided to show the applicability and reduced conservativeness of the present results.

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This paper is concerned with the symmetry reductions of the (3 + 1)-dimensional modified Zakharov-Kuznetsov equation of ion-acoustic waves in a magnetized plasma. The direct symmetry method is applied to determine the symmetry and the corresponding vector field. Then, the considered equation is reduced to lower-dimensional equations with the aid of the obtained symmetry. At last, some exact solutions of the modified Zakharov-Kuznetsov equation are found in terms of the lower-dimensional equations.

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