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In this study, we discuss the global dynamics of the Holling-II amensalism model for a strong Allee effect of harmful species. We discuss the existence and stabilization of the extinction equilibria, exclusion equilibria, coexistence equilibria, and infinite singularities by analyzing the presence and stabilization of the system characteristics in terms of the possibilities and correspondences in the model when the death rate of the injured species is used as a threshold value. Also, we find that the two equilibrium points in the first quadrant are effective in proving that the model does not have globally stabilizing features and obtain two critical conditions and their corresponding global phase diagrams. Finally, we explore the weak Allee effect of the victim species, and using the analysis from numerical simulations, we recapitulate the analysis and dynamics of the model in equilibrium. [ABSTRACT FROM AUTHOR]

The aim of this paper is to establish a precise illustration for the structure of the nonconstant steady states for a Beddington–DeAngelis and Tanner predator–prey reaction–diffusion system with prey‐taxis. We treat the nonlinear prey‐taxis as a bifurcation parameter to analyze the bifurcation structure of the system. Furthermore, the exported global bifurcation theorem, under a rather natural condition, offers the existence of nonconstant steady states. In the proof, a priori estimates of steady states will play an important role. The local stability analysis with a numerical simulation and bifurcation analysis are given. Finally, some conclusions including biological meanings are performed to summarize our main analytic results and future investigations. [ABSTRACT FROM AUTHOR]

Retraction: Luo D, Liang, H. Oscillatory solutions of n‐th order advanced trinomial differential equations. Mathematische Nachrichten. 2018; 1–13. https://doi.org/10.1002/mana.201700219 The above article, published online on 5 October 2018, has been retracted by agreement between the corresponding author, Demou Luo, the journal's Editors‐in‐Chief, R. Denk, B. Andrews, K. Hulek and F. Klopp, and Wiley‐VCH Verlag GmbH & Co. The retraction has been agreed due to the unattributed use of substantial portions of text from an article previously submitted to, but not published in, Mathematische Nachrichten by another author. [ABSTRACT FROM AUTHOR]