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A chaotic parameter-optimized radial basis function (RBF) forecasting model was proposed. The chaos theory was used to obtain the embedded dimension and delay time of the ENPEMF， and the obtained parameters were used to optimize the RBF neural network. Finally， the trained optimized-RBF was utilized to forecast the strength trend of 14 d ENPEMF data. Numerical simulation results show that the improved RBF model could forecast the Rossler time series well with small error. Applying the improved RBF algorithm to the ENPEMF data before Ms7.0 earthquake in Lushan， it can effectively forecast the ENPEMF intensity trend 14 d before earthquake. The forecasting effect and accuracy are significantly better than that of the traditional RBF algorithm， which is expected to provide support for electromagnetic monitoring and analysis before earthquakes and geological disasters. [ABSTRACT FROM AUTHOR]

Compressive sensing is a new sampling theory which makes use of the sparsity of signals to recover the high-dimension signal from very few measurements. Unfortunately,most of the existing measurement matrices have high correlation between elements,which can not guarantee exact recovery and has greatly restricted their application prospects. Based on this,this paper proposed a novel Chebyshev chaotic measurement sensing matrix based on sampling columnization( SC3M). The sampling columnization and normalization guaranteed the low correlation in column of SC3 M,which optimized the recovery effect. Moreover,it proved that the proposed SC3 M sensing matrix satisfies the RIP with overwhelming probability from the Johnson-Lindenstrauss lemma. Numerical simulations show that the SC3 M is sufficient to guarantee exact recovery,which shows better effect compared to other popular measurement matrixes such as the fully random matrix,Bernoulli matrix and Gaussian sensing matrix. [ABSTRACT FROM AUTHOR]

Considering Poisson white noise and Gauss white noise into the intrinsic grow rate of prey and the death rate of predators, a stochastic system of three population densities with Beddington -DeAngelis functional response is established. Then Milstein method is used to make stochastic system discrete and programs is compiled with computer algebra Matlab to finish the analysis. Numerical simulations of deterministic system and stochastic system certifiy the result obtained. The results demonstrate that a bounded chaotic attractor would occur in the stochastic system if the noises are sufficiently small. [ABSTRACT FROM AUTHOR]

Based on the Si' lnikov theorem, this paper proposed a new three-dimensional square chaotic system, which had tow equilibrium poits. There was hyperbolic saddle focus. The formation mechanism showed that this chaotic system had Smale horseshoes (homoclinic chaos). Under satisfying the homoclinic Si' lnikov theorem, the large number of parameter values, which could be found, made that the system was chaotic state. Numerical simulation results show the effectiveness of the theoretical results. Finally, Smale horseshoses had been found in the system using undetermined-coefficient method, and it was chaotic in the sense of Si' lnikov. [ABSTRACT FROM AUTHOR]