Dynamical behaviors for a competition and cooperation model of enterprises with two delays

Nonlinear Dynamics

Volumn 75, Issue 1-2, 2014, Pages 257-266

  Liao, Maoxin ^a   Xu, Changjin ^b   Tang, Xianhua ^c  

^a UNIVERSITY OF SOUTH CHINA   (China)

^b GUIZHOU UNIVERSITY OF FINANCE AND ECONOMICS   (China)

^c CENTRAL SOUTH UNIVERSITY   (China)

Author keywords

Competition; Cooperation; Delay; Dynamical behavior; Enterprise

Indexed keywords

BIFURCATION PARAMETER; BIFURCATION PHENOMENA; COMPETITION AND COOPERATION; COOPERATION; CRITICAL VALUE; DELAY; DYNAMICAL BEHAVIORS; POSITIVE EQUILIBRIUM;

DYNAMICS; HOPF BIFURCATION; INDUSTRY;

COMPETITION;

EID: 84891559020     PISSN: 0924090X     EISSN: None     Source Type: Journal    
DOI: 10.1007/s11071-013-1063-9     Document Type: Article

References (24)

1. Beretta, E.; Kuang, Y.: Convergence results in a well-known delayed predator-prey system. J. Math. Anal. Appl. 204, 840-853 (1996)
2. Cushing, J.M.: Periodic time-dependent predator-prey systems. SIAM J. Appl. Math. 32, 82-95 (1997)
3. Faria, T.: Stability and bifurcation for a delay predator-prey model and the effect of diffusion. J. Math. Anal. Appl. 254, 433-463 (2001)
4. Hale, J.; Lunel, S.V.: Introduction to Functional Differential Equations. Springer, New York (1993)
5. Hassard, B.; Kazarino, D.; Wan, Y.: Theory and Applications of Hopf Bifurcation. Cambridge University Press, Cambridge (1981)
6. Kuang, Y.: Delay Differential Equations with Applications in Population Dynamics. Academic Press, Boston (1993)
7. Song, Y.; Han, M.: Stability and Hopf bifurcation in a competitive Lokta-Volterra system with two delays. Chaos Solitons Fractals 22, 1139-1148 (2004)
8. Song, Y.; Wei, J.: Local Hopf bifurcation and global periodic solutions in a delayed predator-prey system. J. Math. Anal. Appl. 301, 1-21 (2005)
9. Wu, J.: Theory and Applications of Partial Functional Differential Equations. Springer, New York (1996)
10. Sun, C.; Loreau, M.: Dynamics of a three-species food chain model with adaptive traits. Chaos Solitons Fractals 41(5), 2812-2819 (2009)
11. Sun, C.; Han, M.; Lin, Y.; Chen, Y.: Global qualitative analysis for a predator-prey system with delay. Chaos Solitons Fractals 32(4), 1582-1596 (2007)
12. Sun, C.; Han, M.; Lin, Y.: Analysis of stability and Hopf bifurcation for a delayed logistic equation. Chaos Solitons Fractals 31(3), 672-682 (2007)
13. Zhao, T.; Kuang, Y.; Smith, H.L.: Global existence of periodic solutions in a class of delayed Gause-type predator-prey system. Nonlinear Anal. 28, 1373-1394 (1997)
14. Liao, M.X.; Tang, X.H.; Xu, C.J.: Bifurcation analysis for a three-species predator-prey system with two delays. Commun. Nonlinear Sci. Numer. Simul. 17, 183-194 (2012)
15. Liao, M.X.; Tang, X.H.; Xu, C.J.: Dynamics of a competitive Lotka-Volterra system with three delays. Appl. Math. Comput. 217, 10024-10034 (2011)
16. Xu, C.J.: Periodic behavior of competition and corporation dynamical model of two enterprises on time scales. J. Quant. Econ. 29(2), 1-4 (2012)
17. Ruan, S.; Wei, J.: On the zeros of transcendental functions with applications to stability of delay differential equations with two delays. Dyn. Contin. Discrete Impuls. Syst.; Ser. A Math. Anal. 10, 863-874 (2003)
18. Tang, X.H.; Zou, X.F.: $\frac{3}{2}$ -type criteria for global attractivity of Lokta-Volterra competitive system without instantaneous negative feedback. J. Differ. Equ. 186, 420-439 (2002)
19. Tang, X.H.; Zou, X.F.: Global attractivity of non-autonomous Lokta-Volterra competitive system without instantaneous negative feedback. J. Differ. Equ. 192, 502-535 (2003)
20. Tang, X.H.; Cao, D.; Zou, X.F.: Global attractivity of positive periodic solution to periodic Lotka-Volterra competition systems with pure delay. J. Differ. Equ. 228, 580-610 (2006)
21. Dong, T.; Liao, X.: Bogdanov-Takens bifurcation in a tri-neuron BAM neural network model with multiple delays. Nonlinear Dyn. 71(3), 583-595 (2013)
22. Zhang, L.; Guo, S.J.: Hopf bifurcation in delayed van der Pol oscillators. Nonlinear Dyn. 71(3), 555-568 (2013)
23. Mukandavire, Z.; Garira, W.; Chiyaka, C.: Asymptotic properties of an HIV/AIDS model with a time delay. J. Math. Anal. Appl. 330(2), 916-933 (2007)
24. Das, P.; Mukandavire, Z.; Chiyaka, C.; Sen, A.; Mukherjee, D.: Bifurcation and chaos in S-I-S epidemic model. Differ. Equ. Dyn. Syst. 17(4), 393-417 (2009)