RT Journal Article
T1 Dynamic Analysis of a Two-Language Competitive Model with Control Strategies
A1 Nie, Lin-Fei
A1 Teng, Zhi-Dong
A1 Nieto Roig, Juan José
A1 Jung, Il Hyo
K1 Dynamic Analysis
K1 Control Strategies
K1 Competitive model
AB 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.
PB Hindawi Publishing
SN 1024-123X
YR 2013
FD 2013
LK http://hdl.handle.net/10347/21776
UL http://hdl.handle.net/10347/21776
LA eng
NO Nie, L. F., Teng, Z. D., Nieto, J. J., and Jung, I. H. (2013). Dynamic analysis of a two-language competitive model with control strategies. Mathematical Problems in Engineering, 2013.
NO This paper has been partially supported by the Scientific Research Programmes of Colleges in Xinjiang (Grant no. XJEDU2011S08), the Natural Science Foundation of Xinjiang (Grant no. 2011211B08), the National Natural Science Foundation of China (Grants nos. 11001235, 11271312, and 11261056), the China Postdoctoral Science Foundation (Grants nos. 20110491750 and 2012T50836), and the Ministerio de Economia y Competitividad (Spain), Project no. MTM2010-15314 and has been co-financed by the European Community Fund FEDER
DS Minerva
RD 24 abr 2026