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An analytical work on intrinsic localized modes in a two-dimensional Heisenberg ferromagnet on the checkerboard lattice is presented. Taking advantage of an asymptotic method, the governing lattice dynamical equations are reduced to one (2+1) -dimensional nonlinear Schr\"odinger. In our work, we obtain two types of nonlinear localized mode solutions, namely, Brillouin zone center modes and Brillouin zone corner modes. The occurrence conditions for these intrinsic localized modes are given in detail. Especially, we find that the competition between the Dzialozinskii-Moriy interaction and the next-nearest neighbor interaction of the checkerboard ferromagnet has an effect on the local structure of the Brillouin zone corner acoustic mode.

This theoretical work is devoted to investigating laser-irradiated Floquet topological magnon insulators on a two-dimensional checkerboard ferromagnet and corresponding topological phase transitions. It is shown that the checkerboard Floquet topological magnon insulator is able to be transformed from a topological magnon insulator into another one possessing various Berry curvatures and Chern numbers by changing the light intensity. Especially, we also show that both Tamm-like and topologically protected Floquet magnon edge states can exist when a nontrivial gap opens. In addition, our results display that the sign of the Floquet thermal Hall conductivity is also tunable via varying the light intensity of the laser field., Comment: This paper has been published in Physica Letter A

We theoretically investigate nonlinear localized excitations in a Heisenberg honeycomb ferromagnet with a second neighbour Dzialozinskii-Moriya interaction, which has been proved to possess the topological band structure. Using the time-dependent variational principle, we obtain the equation of motion for the system in the Glauber coherent-state representation. By means of the semidiscrete multiple-scale method, different types of nonlinear localized excitations are gotten.Our results show that both two-dimensional discrete breathers and bulk gap solitons may occur in the Heisenberg honeycomb ferromagnet., Comment: This paper has been published in Journal of Magnetism and Magnetic Materials

In this paper we consider the output consensus problem of networked Hammerstein and Wiener systems in a noisy environment. The Hammerstein or Wiener system is assumed to be open-loop stable, and its static nonlinearity is allowed to grow up but not faster than a polynomial. A control algorithm based on the distributed stochastic approximation algorithm with expanding truncations is designed and it is shown that under the designed control the output consensus is achieved. The numerical simulation given in the paper justifies the theoretical assertions., Comment: 19 pages, 7 figures