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In recent years, some researchers paid their attention to the interaction between toxic phytoplankton and zooplankton. Their studies showed that the mechanism of food selection in zooplankton is still immature and when different algae of the same species (toxic and nontoxic) coexist, some zooplankton may not be able to distinguish between toxic and nontoxic algae, and even show a slight preference for toxic strains. Thus, in this article, a fractional order mathematical model with time delay is constructed to describe the interaction of nutrient-phytoplankton-toxic phytoplankton-zooplankton. The main purpose of this paper is to study the influence of fractional order and time delay on the ecosystem. The sufficient conditions for the existence and local stability of each equilibrium are obtained by using fractional order stability theory. By choosing time delay as the bifurcation parameter, we find that Hopf bifurcation occurs when the time delay passes through a sequence of critical values. After that, some numerical simulations are performed to support the analytic results. At last we make some conclusion and point out some possible future work.In this paper, a delayed mathematical model for the P53-Mdm2 network is developed. The P53-Mdm2 network we study is triggered by growth factor instead of DNA damage and the amount of DNA damage is regarded as zero. We study the influences of time delays, growth factor and other important chemical reaction rates on the dynamic behaviors in the system. It is shown that the time delay is a critical factor and its length determines the period, amplitude and stability of the P53 oscillation. Furthermore, as for some important chemical reaction rates, we also obtain some interesting results through numerical simulation. Especially, S (growth factor), k3 (rate constant for Mdm2 p dephosphorylation), k10 (basal expression of PTEN) and k14 (Rate constant for PTEN-induced Akt dephosphorylation) could undermine the dynamic behavior of the system in different degree. These findings are expected to understand the mechanisms of action of several carcinogenic and tumor suppressor factors in humans under normal conditions.This paper revisits the study of numerical approaches for fractional SIRC model with Salmonella bacterial infection (FSIRC-MSBI). This model is investigated by the aid of fully shifted Jacobi's collocation method for temporal discretization. It is concluded that the method of the current paper is far more efficient and reliable for the considered model. Numerical results illustrate the performance efficiency of the algorithm. The results also point out that the scheme can lead to spectral accuracy of the studied model.In this paper, an improved spotted hyena optimizer (ISHO) with a nonlinear convergence factor is proposed for proportional integral derivative (PID) parameter optimization in an automatic voltage regulator (AVR). In the proposed ISHO, an opposition-based learning strategy is used to initialize the spotted hyena individual's position in the search space, which strengthens the diversity of individuals in the global searching process. A novel nonlinear update equation for the convergence factor is used to enhance the SHO's exploration and exploitation abilities. The experimental results show that the proposed ISHO algorithm performed better than other algorithms in terms of the solution precision and convergence rate.We study a quasi-one-dimensional steady-state Poisson-Nernst-Planck type model for ionic flows through a membrane channel with three ion species, two positively charged with the same valence and one negatively charged. Bikerman's local hard-sphere potential is included in the model to account for ion sizes. The problem is treated as a boundary value problem of a singularly perturbed differential system. Under the framework of a geometric singular perturbation theory, together with specific structures of this concrete model, the existence and uniqueness of solutions to the boundary value problem for small ion sizes is established. Furthermore, treating the ion sizes as small parameters, we derive an approximation of individual fluxes, from which one can further study the qualitative properties of ionic flows and extract concrete information directly related to biological measurements. Of particular interest is the competition between two cations due to the nonlinear interplay between finite ion sizes, diffusion coefficients and boundary conditions, which is closely related to selectivity phenomena of open ion channels with given protein structures. Furthermore, we are able to characterize the distinct effects of the nonlinear interplays between these physical parameters. Numerical simulations are performed to identify some critical potentials which play critical roles in examining properties of ionic flows in our analysis.This paper presents an edge detection algorithm based on singular value eigenvector and gradient operator. SB-743921 In the proposed algorithm, the singular values of image blocks are first calculated, and the Sobel gradient template is extended to eight other directions. Then the gradient values of image pixels are determined according to the stability of the singular values of image blocks. The determination of gradient threshold is considered from both global and local aspects. After calculating the global and local gradient thresholds of the original image, the gradient threshold of the whole image is determined by weighting function. Then the edge pixels of the image are filtered according to the gradient threshold, and the edge information image of the original image is obtained. The experimental data show that the proposed algorithm can resist a certain degree of noise interference, and the accuracy and efficiency of edge extraction are better than other similar algorithms.Since December 2019, an outbreak of a novel coronavirus pneumonia (WHO named COVID-19) swept across China. In Shanxi Province, the cumulative confirmed cases finally reached 133 since the first confirmed case appeared on January 22, 2020, and most of which were imported cases from Hubei Province. Reasons for this ongoing surge in Shanxi province, both imported and autochthonous infected cases, are currently unclear and demand urgent investigation. In this paper, we developed a SEIQR difference-equation model of COVID-19 that took into account the transmission with discrete time imported cases, to perform assessment and risk analysis. Our findings suggest that if the lock-down date in Wuhan is earlier, the infectious cases are fewer. Moreover, we reveal the effects of city lock-down date on the final scale of cases if the date is advanced two days, the cases may decrease one half (67, 95% CI 66-68); if the date is delayed for two days, the cases may reach about 196 (95% CI 193-199). Our investigation model could be potentially helpful to study the transmission of COVID-19, in other provinces of China except Hubei.