Volume 66 | Issue 9 | Year 2020 | Article Id. IJMTT-V66I9P511 | DOI : https://doi.org/10.14445/22315373/IJMTT-V66I9P511
SU Xiao-ya, ZHAI Yan-hui, "Stability and Hopf Branch of Partial Profit Model with Three Time Delays," International Journal of Mathematics Trends and Technology (IJMTT), vol. 66, no. 9, pp. 79-98, 2020. Crossref, https://doi.org/10.14445/22315373/IJMTT-V66I9P511
1] Graves W G,Peckham B,Pastor J.A bifurcation analysis of a differential equations model for mutualism[J].Bulletin of Mathematical Biology,2006,68:1851-1872.
[2] Liu Z J,Tan R H,Chen Y P,Chen L S.On the stable periodic solutions of a delayed two-species model of facultative mutualism[J].Applied Mathematics and Computation,2008,196:105-117.
[3] Vargas-De-león C.Lyapunov functions for two-species cooperative systems[J].Applied Mathematics and Computation,2012,219:2493-2497.
[4] Z.Liu,J.Wu,R.Tan,Y.Chen.Modeling and analysis of a periodic delayed two-species model of facultative mutualism[J].Applied Mathematics and Computation,2010,217:893-903.
[5] Li Y,Chen Y Q,Podlubny I.Mittag-Leffler stability of fractional order nonlinear dynamic systems[J].Automatica,2009,45:1965-1969.
[6] Ahmed E,El-Sayed A M A,Hala A.A.El-Saka.On some Routh-Hurwitz conditions for fractional order differential equations and their applications in Lorenz,Rössler,Chua and Chen systems[J].Physics Letters A,2006,358:1-4.
[7] Vargas-De-león C.Volterra-type Lyapunoy functions for fractional-order epidemic systems[J].Commun Nonlinear Sci Numlar,2015,24:75-85.
[8] Delavari H,Baleanu D,Sadati J.Stability analysis of Caputo fractional-order nonlinear stemsc systems revisited[J].Nonlinear Dyn,2012,67:2433-2439.
[9] Aguila-Camacho N,Duarte-Mermoud M A,Gallegos JA.Lvapunov functions for fractional order systems[J].Commun Nonlinear Sci NumerSimul,2014,19:2951-2957.
[10] Jiang Q Y,Xie J X,Ye J.Mathematical Modelling Fourth edition[M].Beijing,Highere Education Press,2011.
[11] B.D.Hassard,N.D.Kazarinoff, Y.H.Wan, Theory and Applications of Hopf Bifurcations,Cambridge University Press,Cambridge.1981.