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Purpose – The purpose of this paper is to analytically solve the (2+1)-dimensional nonlinear time fractional biological population model in the Caputo sense. Design/methodology/approach – The paper uses the variable separation method and the properties of Gamma function to construct exact solutions of the time fractional biological population model. Findings – New variable separation solutions are obtained, from which some known solutions are recovered as special cases. Originality/value – Solving fractional biological population model by the variable separation method and the properties of Gamma function is original. It is shown that the method presented in this paper can be also used for some other nonlinear fractional partial differential equations arising in sciences and engineering. [ABSTRACT FROM AUTHOR]

This paper investigates two intricate problems in magnetic levitation systems: the loss of the information during the transmission over a limited communication network channel and the chattering caused by external disturbances. By combining input quantization technique with two infinitesimal smooth functions, we successfully construct a continuous robust adaptive feedback controller which stabilizes the position of the levitated electromagnet at the equilibrium point. Compared with the existing methods, the proposed quantized control strategy not only guarantees the global stability with asymptotic state regulation of the system even if there are external disturbances, but also exhibits better performance than that of traditional PID control. The simulation validates the robustness and effectiveness of the proposed scheme. [ABSTRACT FROM AUTHOR]

The two-dimensional shallow water equations (SWEs) are a hyperbolic system of first-order nonlinear partial differential equations which have a characteristic of strong gradient. In this study, a newly-developed numerical model, based on local radial point interpolation method (LRPIM), is adopted to simulate discontinuity in shallow water flows. In order to accurately capture the information of wave propagation, the LRPIM is combined with the split-coefficient matrix (SCM) method to transform the SWEs into a characteristic form and the selection of the direction of local support domain is introduced into the LRPIM. An improved meshless artificial viscosity (MAV) technique is developed to minimize the non-physical oscillations near the discontinuities. Then, the LRPIM and the second-order Runge–Kutta method are adopted for spatial and temporal discretization of the SWEs, respectively. The feasibility and validity of the proposed numerical model are verified by the classical dam-break problem and the mixed flow pattern problem. The comparison of the obtained results with the analytical solution and other numerical results showed that the MAV method combined with LRPIM can accurately capture the shocks and has high accuracy in dealing with discontinuous flow by adding appropriate viscosity to the equations in the discontinuous region. [ABSTRACT FROM AUTHOR]

The automatic detection and search of small targets by the infrared guidance system is challenged by the complex sea background environment, particularly the dense scaly light generated by the reflection of sunlight by the sea clutter and the appearance of boundaries. To address this issue, inspired by the significant sensitivity, classification perception, reverse exclusion, and association prediction characteristics of the human visual system, this paper proposes a human vision-inspired detection model for infrared small targets under scaly light background on the sea surface. Firstly, the local energy factor and multi-scale patch contrast measure are fused to construct a significance analysis model and enhance the contrast of the target region of interest. Then, the image is classified into different regions according to the detection of grayscale fluctuations and mutation points in the background, and a region self-classification perception model is constructed for adaptive segmentation of scene images. Next, the prior information of the target gradient is used to construct a reverse exclusion analysis model for suppressing the residual background of the boundary. Subsequently, by using the fluctuation law and characteristic difference of the spatial energy and size features of the target and the scaly light background in the time domain, the correlation prediction analysis model is constructed to further suppress the residual background. Finally, through the combination of the above four visual feature models, a new detector with good adaptability is proposed for small targets under scaly light background on the sea surface. The experimental results indicate that the average detection rate of our detector is 95.26%, and the number of false alarms in a single frame is reduced by 93.77% compared with the typical detectors. [ABSTRACT FROM AUTHOR]