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In a recent paper of Yuan and Zhu (J. Differential Equations 321(2022) 99-129), the nature of dynamics of a generalist predator and prey with stage structure is modeled as a three-dimensional coupled nonlinear differential system. A detailed analysis of the bifurcation shows that the model exhibits a high complexity in its dynamics, which arises from the use of predatory mites as agent for controlling stage structures of tea green leafhopper pest. Unfortunately, there is a mistake in Proposition 2.2, item (3), also the hypothesis in Proposition 3.3 is incorrect. In this paper, we revisit the model and straighten those mentioned errors as in item (3), changed the existing hypothesis by a suitable one and give a corrected proof of Proposition 3.3 in its new form. Also, we show that the model does undergo both Hopf bifurcation and Bautin bifurcation, and numerical examples are given to support the analytic results.

The future space-borne Laser Interferometer Space Antenna (LISA) is expected to detect gravitational waves (GW) from Extreme Mass Ratio Inspiral (EMRI) binaries which may live in nontrivial environments such as accretion disks. In this work, we apply the Fisher matrix Principal Component Analysis (PCA) method to assess how well LISA observations can jointly constrain the source parameters and environmental densities around EMRIs. Specifically, we calculate the Fisher matrix from the post-Newtonian parameters of an EMRI binary embedded in a fluid with a constant density profile. We determine that the most dominant measurable parameter combination is dominated by contributions from environmental effects, namely, gravitational drag, accretion, and gravitational pull (in order of contribution). The proposed reparameterization of the PN parameters can be used to improve the power and efficiency of future detection and parameter estimation methods., Comment: Matches accepted version in New Astronomy; 8 pages, 2 figures