Complex-valued B-spline neural networks for modeling and inverting Hammerstein systems

Many communication signal processing applications involve modelling and inverting complex-valued (CV) Hammerstein systems. We develops a new CV B-spline neural network approach for efficient identification of the CV Hammerstein system and effective inversion of the estimated CV Hammerstein model. Specifically, the CV nonlinear static function in the Hammerstein system is represented using the tensor product from two univariate B-spline neural networks. An efficient alternating least squares estimation method is adopted for identifying the CV linear dynamic model’s coefficients and the CV B-spline neural network’s weights, which yields the closed-form solutions for both the linear dynamic model’s coefficients and the B-spline neural network’s weights, and this estimation process is guaranteed to converge very fast to a unique minimum solution. Furthermore, an accurate inversion of the CV Hammerstein system can readily be obtained using the estimated model. In particular, the inversion of the CV nonlinear static function in the Hammerstein system can be calculated effectively using a Gaussian-Newton algorithm, which naturally incorporates the efficient De Boor algorithm with both the B-spline curve and first order derivative recursions. The effectiveness of our approach is demonstrated using the application to equalisation of Hammerstein channels.

Modeling migratory grazing of zooplankton on toxic and non-toxic phytoplankton

Migratory grazing of zooplankton between non-toxic phytoplankton (NTP) and toxic phytoplankton (TPP) is a realistic phenomena unexplored so far. The present article is a first step in this direction. A mathematical model of NTP–TPP-zooplankton with constant and variable zooplankton migration is proposed and analyzed. The asymptotic dynamics of the model system around the biologically feasible equilibria is explored through local stability analysis. The dynamics of the proposed system is explored and displayed for different combination of migratory parameters and toxin inhibition parameters. Our analysis suggests that the migratory grazing of zooplankton has a significant role in determining the dynamic stability and oscillation of phytoplankton zooplankton systems.

The response of the magnetosphere-ionosphere system to solar wind dynamic pressure variations

We study the causal chain of events by which variations in the solar wind dynamic pressure cause the magnetopause boundary to move and excite magnetic perturbations at the ground. The observation of large ground magnetic transients is argued to be due to the coupling of the magnetohydrodynamic compressional wave to the field-guided Alfvén wave, which carrying current, can thereby transfer momentum to the ionosphere. The study highlights the similarity of the ionospheric signatures at a single station arising from the response of the coupled magnetosphere-ionosphere system to disparate impulsive processes at the magnetopause.