Dynamic Analysis of a Two-Language Competitive Model with Control Strategies
Joint Authors
Nie, Lin-Fei
Teng, Zhidong
Nieto, Juan Jose
Jung, Il Hyo
Source
Mathematical Problems in Engineering
Issue
Vol. 2013, Issue 2013 (31 Dec. 2013), pp.1-13, 13 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2013-12-03
Country of Publication
Egypt
No. of Pages
13
Main Subjects
Abstract EN
The dynamic behavior of a two-language competitive model is analyzed systemically in this paper.
By the linearization and the Bendixson-Dulac theorem on dynamical system, some sufficient conditions on the globally asymptotical stability of the trivial equilibria and the existence and the stability of the positive equilibrium of this model are presented.
Nextly, in order to protect the endangered language, an optimal control problem relative to this model is explored.
We derive some necessary conditions to solve the optimal control problem and present some numerical simulations using a Runge-Kutta fourth-order method.
Finally, the languages competitive model is extended to this model assessing the impact of state-dependent pulse control strategy.
Using the Poincaré map, differential inequality, and method of qualitative analysis, we prove the existence and stability of positive order-1 periodic solution for this control model.
Numerical simulations are carried out to illustrate the main results and the feasibility of state-dependent impulsive control strategy.
American Psychological Association (APA)
Nie, Lin-Fei& Teng, Zhidong& Nieto, Juan Jose& Jung, Il Hyo. 2013. Dynamic Analysis of a Two-Language Competitive Model with Control Strategies. Mathematical Problems in Engineering،Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-1010252
Modern Language Association (MLA)
Nie, Lin-Fei…[et al.]. Dynamic Analysis of a Two-Language Competitive Model with Control Strategies. Mathematical Problems in Engineering No. 2013 (2013), pp.1-13.
https://search.emarefa.net/detail/BIM-1010252
American Medical Association (AMA)
Nie, Lin-Fei& Teng, Zhidong& Nieto, Juan Jose& Jung, Il Hyo. Dynamic Analysis of a Two-Language Competitive Model with Control Strategies. Mathematical Problems in Engineering. 2013. Vol. 2013, no. 2013, pp.1-13.
https://search.emarefa.net/detail/BIM-1010252
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1010252