New Stability Criterion for Takagi-Sugeno Fuzzy Cohen-Grossberg Neural Networks with Probabilistic Time-Varying Delays

A new global asymptotic stability criterion of Takagi-Sugeno fuzzy Cohen-Grossberg neural networks with probabilistic time-varying delays was derived, in which the diffusion item can play its role. Owing to deleting the boundedness conditions on amplification functions, the main result is a novelty to some extent. Besides, there is another novelty in methods, for Lyapunov-Krasovskii functional is the positive definite form of p powers, which is different from those of existing literature. Moreover, a numerical example illustrates the effectiveness of the proposed methods

LMI Approach to Exponential Stability and Almost Sure Exponential Stability for Stochastic Fuzzy Markovian-Jumping Cohen-Grossberg Neural Networks with Nonlinear p-Laplace Diffusion

The robust exponential stability of delayed fuzzy Markovian-jumping Cohen-Grossberg neural networks (CGNNs) with nonlinear p-Laplace diffusion is studied. Fuzzy mathematical model brings a great difficulty in setting up LMI criteria for the stability, and stochastic functional differential equations model with nonlinear diffusion makes it harder. To study the stability of fuzzy CGNNs with diffusion, we have to construct a Lyapunov-Krasovskii functional in non-matrix form. But stochastic mathematical formulae are always described in matrix forms. By way of some variational methods in W1,p(Ω), Itô formula, Dynkin formula, the semi-martingale convergence theorem, Schur Complement Theorem, and LMI technique, the LMI-based criteria on the robust exponential stability and almost sure exponential robust stability are finally obtained, the feasibility of which can efficiently be computed and confirmed by computer MatLab LMI toolbox. It is worth mentioning that even corollaries of the main results of this paper improve some recent related existing results. Moreover, some numerical examples are presented to illustrate the effectiveness and less conservatism of the proposed method due to the significant improvement in the allowable upper bounds of time delays

LMI-Based Stability Criterion for Impulsive CGNNs via Fixed Point Theory

Linear matrices inequalities (LMIs) method and the contraction mapping theorem were employed to prove the existence of globally exponentially stable trivial solution for impulsive Cohen-Grossberg neural networks (CGNNs). It is worth mentioning that it is the first time to use the contraction mapping theorem to prove the stability for CGNNs while only the Leray-Schauder fixed point theorem was applied in previous related literature. An example is given to illustrate the effectiveness of the proposed methods due to the large allowable variation range of impulse

Implicit Iteration Process for Common Fixed Points of Strictly Asymptotically Pseudocontractive Mappings in Banach Spaces

In this paper, a new implicit iteration process with errors for finite families of strictly asymptotically pseudocontractive mappings and nonexpansive mappings is introduced. By using the iterative process, some strong convergence theorems to approximating a common fixed point of strictly asymptotically pseudocontractive mappings and nonexpansive mappings are proved. The results presented in the paper are new which extend and improve some recent results of Osilike et al. (2007), Liu (1996), Osilike (2004), Su and Li (2006), Gu (2007), Xu and Ori (2001)

Field-Scale Spatial Variation of Saline-Sodic Soil and Its Relation with Environmental Factors in Western Songnen Plain of China

The objectives of this study were to investigate the degree of spatial variability and variance structure of salinization parameters using classical and geostatistical method in Songnen Plain of China, which is one of largest saline-sodic areas in the World, and to analyze the relationship between salinization parameters, including soil salinity content (SC), electrical conductivity (EC), sodium adsorption ratio (SAR), and pH, and seven environmental factors by Pearson and stepwise regression analysis. The environmental factors were ground elevation, surface ponding time, surface ponding depth, and soil moistures at four layers (0–10 cm, 10–30 cm, 30–60 cm, and 60–100 cm). The results indicated that SC, EC, and SAR showed great variations, whereas pH exhibited low variations. Four salinization parameters showed strongly spatial autocorrelation resulting from the compound impact of structural factors. The empirical semivariograms in the four parameters could be simulated by spherical and exponential models. The spatial distributions of SC, EC, SAR and pH showed similar patterns, with the coexistence of high salinity and sodicity in the areas with high ground elevation. By Pearson analysis, the soil salinization parameters showed a significant positive relationship with ground elevation, but a negative correlation with surface ponding time, surface ponding depth, and soil moistures. Both correlation and stepwise regression analysis showed that ground elevation is the most important environmental factor for spatial variation of soil sanilization. The results from this research can provide some useful information for explaining mechanism of salinization process and utilization of saline-sodic soils in the Western Songnen Plain