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During this analysis, as per natural control approach in pest management, a plant-pest dynamics with biological control is proposed, here assuming that the pest and natural enemy are having different levels of gestation delay and harvesting rate of pests by natural enemy follows Holling type-III response function. Boundedness and positivity of the system are studied. Equilibria and stability analysis is carried out for possible equilibrium points. The existence of Hopf bifurcation at interior equilibrium is presented. The sensitivity analysis of the system at interior equilibrium point for model parameters has been explored. Numerical simulations are performed to support our analytic findings.

An estimated initial stiffness matrix is generally needed to determine the coefficient matrices of quadrature equations for a structure-dependent pseudodynamic algorithm. It is shown herein that an experimentally determined initial stiffness matrix is, in general, close to the true initial stiffness matrix if an imposed displacement is small enough. This case is often encountered in practice. The case where an estimated initial stiffness is different from a true initial stiffness for employing a structure-dependent pseudodynamic algorithm is also explored. The numerical properties and error propagation properties are evaluated as a function of the initial stiffness ratio, which is the ratio of an estimated initial stiffness over a true initial stiffness. In general, accuracy and error propagation properties are insensitive to the initial stiffness ratio. It seems that the change of bifurcation point between unconditional stability and conditional stability is of worth noting. In order to avoid this stability problem, guidelines are recommended if a structure-dependent pseudodynamic algorithm is used.

With the recurrence of extreme weather events in Central Africa, it becomes imperative to provide high-resolution forecasts for better decision-making by the Early warning systems. This study assesses the performance of the Weather Research and Forecasting (WRF) model to simulate heavy rainfall that affected the city of Douala in Cameroon during 19–21 August 2020. The WRF model is configured with two domains with horizontal resolutions of 15 and 5km, 33 vertical levels using eight cumulus parameterization schemes (CPSs). The WRF model performance is assessed by investigating the agreement between simulations and observations. Categorical and deterministic statistics are used, which include the probability of detection (POD), the success ratio (SR), the equitable threat score (ETS), the pattern correlation coefficient (PCC), the root mean square error (RMSE), the mean absolute error (MAE), and the BIAS. K-index is finally used to assess the capacity of the WRF model to predict the instability of the atmosphere in Douala during the above-mentioned period. It is found that (1) The POD, SR and ETS decrease when the threshold increases, showing the difficulty of the WRF model to predict and locate heavy rainfall events; (2) There are important differences in the rainfall area simulated by the eight CPSs; (3) The BIAS is negative for the eight CPSs, implying that all of the CPSs tested underestimate the rainfall over the study area; (4) Some of the CPSs have good agreement with observations, especially the new modifed Tiedtke and the Betts–Miller–Janjic schemes; (5) The K-index, an atmospheric instability index, is well predicted by the eight CPSs tested in this work. Overall, the WRF model exhibits a strong ability for rainfall simulation in the study area. The results point out that heavy rainfall events in tropical areas are very sensitive to CPSs and study domain. Therefore, sensitivity tests studies should be multiplied in order to identify most suitable CPSs for a given area.