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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

We consider a reconstructing scheme using observational data from SNIa, BAO and CMB, based on a model of dark unification using a single non-minimally coupled scalar field. We investigate through a reconstruction program, the main features the current observational data imposes to the scalar field potential. We found that the form suggested by observations implies a step feature in the potential, where the kinetic and potential energy becomes of the same order of magnitude., Comment: Proceedings of I CosmoSul - Cosmology and Gravitation in Southern Cone (Rio de Janeiro, 2011). Eds: J. S. Alcaniz, S. Carneiro, L. P. Chimento, S. del Campo, J. C. Fabris, J. A. S. Lima and W. Zimdahl

We introduce the curvature $\Omega_k$ as a new free parameter in the Bayesian analysis using SNIa, BAO and CMB data, in a model with variable equation of state parameter $w(z)$. We compare the results using both the Constitution and Union 2 data sets, and also study possible low redshift transitions in the deceleration parameter $q(z)$. We found that, incorporating $\Omega_k$ in the analysis, it is possible to make all the three observational probes consistent using both SNIa data sets. Our results support dark energy evolution at small redshift, and show that the tension between small and large redshift probes is ameliorated. However, although the tension decreases, it is still not possible to find a consensus set of parameters that fit all the three data set using the Chevalier-Polarski-Linder CPL parametrization., Comment: 6 pages, 8 figures