Dr. Kai Wang

University: Anhui University of Finance and Economics
Department: Department of Applied Mathematics
Research Fields: Differential equation Dynamic system Mathematical Biology

Publications

4 Permanence and Global Attractivity of a Delayed Predator-Prey Model with Mutual Interference

Authors: Kai Wang, Yanling Zu

Abstract:

By utilizing the comparison theorem and Lyapunov second method, some sufficient conditions for the permanence and global attractivity of positive periodic solution for a predator-prey model with mutual interference m ∈ (0, 1) and delays τi are obtained. It is the first time that such a model is considered with delays. The significant is that the results presented are related to the delays and the mutual interference constant m. Several examples are illustrated to verify the feasibility of the results by simulation in the last part.

Keywords: delays, predator-prey model, mutual interference, permanence, Global attractivity

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3 Positive Periodic Solutions for a Predator-prey Model with Modified Leslie-Gower Holling-type II Schemes and a Deviating Argument

Authors: Yanling Zhu, Kai Wang

Abstract:

In this paper, by utilizing the coincidence degree theorem a predator-prey model with modified Leslie-Gower Hollingtype II schemes and a deviating argument is studied. Some sufficient conditions are obtained for the existence of positive periodic solutions of the model.

Keywords: predator-prey model, Holling II type functional response, positive periodic solution, coincidence degree theorem

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2 Permanence and Exponential Stability of a Predator-prey Model with HV-Holling Functional Response

Authors: Kai Wang, Yanling Zu

Abstract:

In this paper, a delayed predator-prey system with Hassell-Varley-Holling type functional response is studied. A sufficient criterion for the permanence of the system is presented, and further some sufficient conditions for the global attractivity and exponential stability of the system are established. And an example is to show the feasibility of the results by simulation.

Keywords: delay, exponential stability, Predator-prey system, permanence, Hassell-Varley-Holling

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1 Periodic Solutions for a Third-order p-Laplacian Functional Differential Equation

Authors: Yanling Zhu, Kai Wang

Abstract:

By means of Mawhin’s continuation theorem, we study a kind of third-order p-Laplacian functional differential equation with distributed delay in the form: ϕp(x (t)) = g  t,  0 −τ x(t + s) dα(s)  + e(t), some criteria to guarantee the existence of periodic solutions are obtained.

Keywords: periodic solution, distributed delay, p–Laplacian, Mawhin's continuation theorem

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Abstracts

1 In situ Investigation of PbI₂ Precursor Film Formation and Its Subsequent Conversion to Mixed Cation Perovskite

Authors: Dounya Barrit, Ming-Chun Tang, Hoang Dang, Kai Wang, Detlef-M. Smilgies, Aram Amassian

Abstract:

Several deposition methods have been developed for perovskite film preparation. The one-step spin-coating process has emerged as a more popular option thanks to its ability to produce films of different compositions, including mixed cation and mixed halide perovskites, which can stabilize the perovskite phase and produce phases with desired band gap. The two-step method, however, is not understood in great detail. There is a significant need and opportunity to adopt the two-step process toward mixed cation and mixed halide perovskites, but this requires deeper understanding of the two-step conversion process, for instance when using different cations and mixtures thereof, to produce high-quality perovskite films with uniform composition. In this work, we demonstrate using in situ investigations that the conversion of PbI₂ to perovskite is largely dictated by the state of the PbI₂ precursor film in terms of its solvated state. Using time-resolved grazing incidence wide-angle X-Ray scattering (GIWAXS) measurements during spin coating of PbI₂ from a DMF (Dimethylformamide) solution we show the film formation to be a sol-gel process involving three PbI₂-DMF solvate complexes: disordered precursor (P₀), ordered precursor (P₁, P₂) prior to PbI₂ formation at room temperature after 5 minutes. The ordered solvates are highly metastable and eventually disappear, but we show that performing conversion from P₀, P₁, P₂ or PbI₂ can lead to very different conversion behaviors and outcomes. We compare conversion behaviors by using MAI (Methylammonium iodide), FAI (Formamidinium Iodide) and mixtures of these cations, and show that conversion can occur spontaneously and quite rapidly at room temperature without requiring further thermal annealing. We confirm this by demonstrating improvements in the morphology and microstructure of the resulting perovskite films, using techniques such as in situ quartz crystal microbalance with dissipation monitoring, SEM and XRD.

Keywords: perovskite solar cell, sol-gel process, in situ GIWAXS, lead iodide, mixed cation, solvate phase

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