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It has been shown that Allee effect can change predator-prey dynamics and impact species persistence. Allee effect in the prey population has been widely investigated. However, the study on the Allee effect in the predator population is rare. In this paper, we investigate the spatiotemporal dynamics of a diffusive predator-prey model with digestion delay and Allee effect in the predator population. The conditions of stability and instability induced by diffusion for the positive equilibrium are obtained. The effect of delay on the dynamics of system has three different cases: (a) the delay doesn't change the stability of the positive equilibrium, (b) destabilizes and stabilizes the positive equilibrium and induces stability switches, or (c) destabilizes the positive equilibrium and induces Hopf bifurcation, which is revealed (numerically) to be corresponding to high, intermediate or low level of Allee effect, respectively. To figure out the joint effect of delay and diffusion, we carry out Turing-Hopf bifurcation analysis and derive its normal form, from which we can obtain the classification of dynamics near Turing-Hopf bifurcation point. Complex spatiotemporal dynamical behaviors are found, including the coexistence of two stable spatially homogeneous or inhomogeneous periodic solutions and two stable spatially inhomogeneous quasi-periodic solutions. It deepens our understanding of the effects of Allee effect in the predator population and presents new phenomena induced be delay with spatial diffusion. [ABSTRACT FROM AUTHOR]

Recent studies demonstrate that the reproduction of prey is suppressed by the fear of predators. However, it will not respond immediately to fear, but rather reduce after a time lag. We propose a diffusive predator-prey model incorporating fear response delay into prey reproduction. Detailed bifurcation analysis reveals that there are three different cases for the effect of the fear response delay on the system: it might have no effect, both stabilizing and destabilizing effect, or destabilizing effect on the stability of the positive equilibrium, respectively, which are found by numerical simulations to correspond to low, intermediate or high level of fear. For the second case, through ordering the critical values of Hopf bifurcation, we prove the existence of stability switches for the system. Double Hopf bifurcation analysis is carried out to better understand how the fear level and delay jointly affect the system dynamics. Using the normal form method and center manifold theory, we derive the normal form of double Hopf bifurcation, and obtain bifurcation sets around double Hopf bifurcation points, from which all the dynamical behaviors can be explored, including periodic solutions, quasi-periodic solutions and even chaotic phenomenon. [ABSTRACT FROM AUTHOR]

A novel heterojunction photocatalyst p-LaFeO3/n-Ag3PO4 has been prepared via a facile in situ precipitation method. It exhibits higher activity than individual Ag3PO4 and LaFeO3 in the degradation of phenol. The excellent activity is mainly attributed to its more effective separation of electron–hole pairs. [ABSTRACT FROM AUTHOR]

Context: In clinical practice, heart failure with concurrent tumors is relatively rare, and surgical intervention is the primary treatment. However, most patients have poor physical function and metabolic capacity, making them less tolerant of surgical trauma. Strengthening perioperative nursing care is therefore particularly important., Objective: The study aimed to analyze the clinical effects of and patient satisfaction with evidence-based nursing interventions on perioperative conditions and quality of life for heart-failure patients with concurrent tumors, with the goal of identifying the optimal nursing model for these patients., Design: The research team conducted a randomized, controlled clinical trial., Setting: The study took place at the First People's Hospital of Lin'an District in Hangzhou City, Zhejiang Province, China., Participants: Participants were 100 heart-failure patients with concurrent tumors who had been admitted to the hospital between July 2021 and July 2022., Interventions: The research team divided participants into two groups based on their admission times with 50 participants in each group: (1) a control group, who received routine nursing care, and (2) an intervention group, who received an evidence-based nursing intervention., Outcome Measures: The research team: (1) examined perioperative conditions, (2) measured changes in plasma levels of brain natriuretic peptide (BNP), (3) evaluated quality of life, and (4) assessed nursing satisfaction nursing satisfaction., Results: No significant differences existed in the groups' demographic and clinical characteristics, indicating comparability. Compared to the control group, the intervention group's: (1) operation time (P = .021), ascending aorta occlusion time (P = .032), turnaround time of cardiopulmonary bypass (P = .040) were significantly shorter; (2) plasma BNP levels were significantly lower at postoperative days 3 (P = .036) and 7 (P = .022); (3) scores for quality of life-physiological (P = .007), emotional (P = .008), social (P = .013), and role (P = .011) function-were significantly higher; and (4) nursing satisfaction was significantly higher (P = .004)., Conclusions: The adoption of evidence-based nursing interventions in clinical settings, especially for heart-failure patients with concurrent tumors, can yield significant effects, improving patient outcomes and enhancing quality of life and nursing satisfaction.

In this paper, the dynamics of a modified Leslie-Gower predator-prey system with two delays and diffusion is considered. By calculating stability switching curves, the stability of positive equilibrium and the existence of Hopf bifurcation and double Hopf bifurcation are investigated on the parametric plane of two delays. Taking two time delays as bifurcation parameters, the normal form on the center manifold near the double Hopf bifurcation point is derived, and the unfoldings near the critical points are given. Finally, we obtain the complex dynamics near the double Hopf bifurcation point, including the existence of quasi-periodic solutions on a 2-torus, quasi-periodic solutions on a 3-torus, and strange attractors.