Author
Shengbin Yu
Other affiliations: Fuzhou University
Bio: Shengbin Yu is an academic researcher from Fujian Normal University. The author has contributed to research in topics: Singularity & Exponential stability. The author has an hindex of 5, co-authored 8 publications receiving 99 citations. Previous affiliations of Shengbin Yu include Fuzhou University.
Papers
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TL;DR: In this article, a predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response is studied, and the local stability of the equilibria and the permanence of the system are investigated.
Abstract: A predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response is studied. The local stability of the equilibria and the permanence of the system are investigated. By applying the fluctuation lemma, qualitative analysis and Lyapunov direct method, respectively, three sufficient conditions on the global asymptotic stability of a positive equilibrium are obtained. MSC:34D23, 92D25, 34D20, 34D40.
43 citations
TL;DR: In this paper, the predator-prey model proposed by Aziz-Alaoui and Okiye was investigated and sufficient conditions on the global asymptotic stability of a positive equilibrium were provided by employing the fluctuation Lemma and Lyapunov direct method, respectively.
Abstract: We study the predator-prey model proposed by Aziz-Alaoui and Okiye (Appl. Math. Lett. 16 (2003) 1069–1075) First, the structure of equilibria and their linearized stability is investigated. Then, we provide two sufficient conditions on the global asymptotic stability of a positive equilibrium by employing the Fluctuation Lemma and Lyapunov direct method, respectively. The obtained results not only improve but also supplement existing ones.
35 citations
TL;DR: In this paper, a non-autonomous discrete competition system with nonlinear interinhibition terms and feedback controls was considered, and the extinction of one of the two species and the corresponding feedback control variables were analyzed.
Abstract: We consider a nonautonomous discrete competition system with nonlinear interinhibition terms and feedback controls. By constructing a suitable Lyapunov function, we obtain some criteria about the extinction of one of the two species and the corresponding feedback controls varieties. Our conclusions not only supplement but also improve some existing ones. Numerical simulations are used to illustrate our analytic analysis. We show that feedback control variables play an important role in the extinction property of the system.
15 citations
TL;DR: Under certain assumptions on V and f, the existence and uniqueness of positive solution for λ > 0 are shown by using variational method and asymptotic behavior of solutions as λ → 0 is studied.
9 citations
TL;DR: In this paper, a new set of sufficient conditions for the permanence of a ratio-dependent predator-prey system with Holling type III functional response and feedback controls are obtained.
Abstract: A new set of sufficient conditions for the permanence of a ratio-dependent predator-prey system with Holling type III functional response and feedback controls are
obtained. The result shows that feedback control variables have no influence on the
persistent property of the system, thus improving and supplementing the main result
of Yang (2008).
5 citations
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TL;DR: In this article, a stochastic predator-prey system with modified Leslie-Gower and Holling-type II schemes with Levy jumps is considered, and the results show that the Levy jumps can change the properties of the population systems significantly.
Abstract: This paper is concerned with a stochastic predator–prey system with modified Leslie–Gower and Holling-type II schemes with Levy jumps. First, we prove there is a unique positive solution to the system with a positive initial value. Then we establish the sufficient conditions for stability in mean and extinction of the system. Finally, we introduce some numerical simulations to support the main results. The results shows that the Levy jumps can change the properties of the population systems significantly.
114 citations
TL;DR: The role of prey refuge and degree of mutual interference among predators in the dynamics of system are investigated and Hopf bifurcation occurs when the delay parameter τ crosses some critical value.
52 citations
TL;DR: In this article, a two species amensalism model with Beddington-DeAngelis functional response is proposed and studied and the existence and stability of possible equilibria are investigated.
Abstract: A two species amensalism model with Beddington–DeAngelis functional response is proposed and studied in this paper. The existence and stability of possible equilibria are investigated. Under some additional assumptions, there are two stable equilibria which implies this system is not asymptotically stable. Based on the stability analysis of equilibria, closed orbits and the saddle connection, we give some comprehensive bifurcation and global dynamics of the system. Next, we further incorporate the Allee effect into the second species and provide a complete qualitative and bifurcation analysis of the system with Allee effect. Numerical simulations show that the system with an Allee effect must take a longer time to reach its stable steady-state solution than that without Allee effect. There is a good agreement between the present results and the numeric simulations.
51 citations
TL;DR: A modified Leslie–Gower predator–prey model with Holling-type II schemes and a prey refuge is proposed and sufficient conditions on the global attractivity of a positive equilibrium are obtained.
Abstract: We propose a modified Leslie–Gower predator–prey model with Holling-type II schemes and a prey refuge. The structure of equilibria and their linearized stability is investigated. By using the iterative technique and further precise analysis, sufficient conditions on the global attractivity of a positive equilibrium are obtained. Our results not only supplement but also improve some existing ones. Numerical simulations show the feasibility of our results.
43 citations
TL;DR: In this article, a predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response is studied, and the local stability of the equilibria and the permanence of the system are investigated.
Abstract: A predator-prey model with modified Leslie-Gower and Beddington-DeAngelis functional response is studied. The local stability of the equilibria and the permanence of the system are investigated. By applying the fluctuation lemma, qualitative analysis and Lyapunov direct method, respectively, three sufficient conditions on the global asymptotic stability of a positive equilibrium are obtained. MSC:34D23, 92D25, 34D20, 34D40.
43 citations