1. Full name:     Tran Dinh Tuong                                   2. Sex: Male

3. Date of birth: 17/10/1978                                            4. Place of birth: Binh Dinh.

5. Admission decision number: Decision 4438/QĐ-ĐHKHTN, dated on 26/11/2015 by Rector of VNU University of Science.

6. Changes in academic process: Decision 4735/QĐ-ĐHKHTN, dated on 28/12/2018 by Rector of VNU University of Science on extending 12 months from the deadline of studying.

7. Official thesis title: Asymptotic behavior of population models in ecosystem with random environment.

8. Major: Differential and Integral Equation                      9. Code: 9460101.03

10. Supervisors: Prof. Dr. Nguyen Huu Du and Assoc.Prof.Dr. Nguyen Thanh Dieu.

11. Summary of the new findings of the thesis

In this thesis, we have studied effect of the random perturbations on some biological systems: the predator-prey systems and an SIRS epidemic evolution. Our main results of this thesis can be summarized as follows.

            For the stochastic predator-systems:

            Finding the thresholds to classify the asymptotic behavior these systems. In the sequel, we aim to provide not only sufficient conditions but also almost necessary condition for permanence, as well as ergodicity of the systems. 

            Estimating (improving) the estimation of convergence of the prey species x(t) to its solution on the boundary equation. 

            Finding conditions for the existence of the stationary distributions and the conditions for the validity of the strong law of larger numbers.

            For the stochastic SIRS model in regime switching with general incidence rate:

            Finding the threshold to classify the asymptotic behavior of the system.

            Obtaining conditions for strongly stochastically permanent of the disease.

12. Practical applicability, if any: The results of this thesis on predator-prey models, epidemic model can be applied to practical problems in biology, economics, life sciences, preventive medicine, …Moreover, our results can help biologists to pinpoint how environmental fluctuations affect the long-term dynamics of ecological/epidemiological communities and then facilitate inference, prediction and estimation using data sets from real world problems in ecology and infectious disease.

13. Further research directions, if any:

In the future, we would like to consider the critical case (λ=0) in some particular cases.  Moreover, we will focus on hybrid switching diffusion systems with Lévy noise. Also, we plan on considering the class of regime switching diffusion systems with switching states x-dependent generator.

14. Thesis-related publications:

[1] N. H. Du, N. T. Dieu, T. D. Tuong (2017), “Dynamics behavior of a stochastic predator-prey system under regime switching'”, Discrete Contin. Dyn. Syst. Ser. B 22 (9), trang 3483-3498.

[2] T. D. Tuong, N. H. Dang, N. T. Dieu, T. Q. Ky (2019), “Extinction and permanence in a stochastic SIRS model in regime switching with general incidence rate”, Nonlinear Anal. Hybrid Syst.  34, trang 121-130.

[3] T. D. Tuong, N. T. Dieu, N. H. Du, “On the asymptotic behavior of a stochastic model with Ivlev's functional response and jumps'', Stochastic Models (revised).