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1. Full name: Tong Thanh Trung
2. Sex: Male
3. Date of birth: 20/11/1975
4. Place of birth: Hanoi
5. Admission of decision number: 212/SĐH, Dated 12 August 2004 by President of Vietnam National University, Hanoi, Form of training is not focused, 3 year term (2004-2007) and 272/SĐH, Dated 22 November 2004 by Rector of Hanoi University of Science on the recognition of doctoral thesis and supervisors.
6. Changes in academic process: Decision 1929/SĐH, Dated 31 December 2007 by Rector of Hanoi University of Science on Extending 12 months from the deadline of Studying.
7. Official thesis title:
Asymptotical behavior of population dynamics
described by differential equations
8. Major: Differential and Integral equations
9. Code: 62 46 01 05.
10. Supervisors: Prof. Dr. Nguyen Huu Du and Dr. Trinh Tuan Anh
11. Summary of the new findings of the thesis:
Obtained some sufficient criteria for dissipativity, persistence, permanence of ecological models.
Generalize the predator–prey models with Beddington–DeAngelis functional response and proved existence their periodic solution.
Showed that some sufficient criteria for globally asymptotically stable of ecological models.
Presented the conditions ensuring existence and uniqueness of positive bounded solution, positive periodic and almost periodic solution of population described by linear and non-linear differential equations.
Showed a stability radii formula of age–structured population described by homogeneous Lotka–Von Foerster system and the classical model of linear age-dependent population dynamics of Sharpe-Lotka-Mc Kendrick.
Furthermore, we illustrated the results by some numerical solutions for our systems.
12. Practical applicability: The models dealt with in this thesis can be use to predict population densities depending on the aged-structure and on the every region. We can also use these results to predict the classification of degree and position of a part of the population in their age.
13. Further research directions, if any:
a. Research properties of solution of the other ecological linear and nonlinear models.
b. Finding to the necessary and sufficient conditions for permanent, global asymptotic stability. The existence and uniqueness of positive bounded solution of differential equations is established by the different models of ecosystem.
c. Finding to the new methods to study permanent, globally asymptotically stable, the existence and unique of positive bounded solution, positive periodic and almost periodic solutions of differential equations for different ecological models.
d. Studying the bifurcation theory for population in the ecosystem described differential equations.
e. Using the mathematical tools to study similar models in economic dynamics.
14. Thesis-related publications:
1. Nguyen Van Minh and Tong Thanh Trung, “On the asymptotic behavior of age-structured populations modeled by Lotka–Von Foerster equations”, Vietnam Journal of Mathematical Applications, Number 1, Vol 1(2003).
2. Nguyen Huu Du, Nguyen Minh Man and Tong Thanh Trung, “Dynamics of predator-prey population with modified Leslie-Gower and Holling-type II schemes”, Acta Mathematica Vietnamica, 32(2007), 99-111.
3. Nguyen Huu Du and Tong Thanh Trung, “On the dynamics of predator-prey systems with Beddington-DeAngelis functional response”, Asian European Journal of Mathematics, Vol 4. No. 1(2011), 35-48.
4. Tong Thanh Trung, “Stability radii of age-structured population described by the homogeneous Lotka-Von Foerster system”, Vietnam Journal of Mathematical Applications, (2010), Submitted, 10 pp.
5. Trinh Tuan Anh, Nguyen Huu Du and Tong Thanh Trung, “On the permanence of predator-prey model with the Beddington-DeAngelis functional response in periodic environment”, Acta Mathematica Vietnamica, (2010), Preprint, 14 pp.
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