RESUMO
In this paper, we investigate the spatial property of the non-integrable discrete defocusing Hirota equation utilizing a planar nonlinear discrete dynamical map method. We construct the periodic orbit solutions of the stationary discrete defocusing Hirota equation. The behavior of the orbits in the vicinity of the special periodic solution is analyzed by taking advantage of the named residue. We characterize the effects of the parameters on the aperiodic orbits with the aid of numerical simulations. A comparison with the non-integrable discrete defocusing nonlinear Schrödinger equation case reveals that the non-integrable discrete defocusing Hirota equation has more abundant spatial properties. Rather an interesting and novel thing is that for any initial value, there exists triperiodic solutions for a reduced map.
RESUMO
This article focuses on the distributed maximum correntropy filtering issue for general stochastic nonlinear systems subject to deception attacks. The considered nonlinear functions consist of a determined one and a stochastic one, and the stochastic signals sent by deception attacks with identified statistic characteristics could be non-Gaussian. The corresponding calculation formulas of both the filter gains and the upper bound of the filter error covariance are proposed by means of the Taylor series expansion and the fixed-point iterative update rule, where the weighted maximum correntropy criterion is utilized to take the place of traditional minimum covariance indexes. Such an upper bound is only dependent on the local information, neighbor information, and the identified statistics of deception attacks and, therefore, the developed filtering scheme realizes the requirement of distributed calculation. Furthermore, a simplified version is obtained by removing weights in the correntropy criterion. Finally, an illustrative example is given to verify the effectiveness of developed distributed maximum correntropy filtering subject to deception attacks.
