Global behavior of a class of three-dimensional competitive systems
Tóm tắt
In this paper the global behavior of a class of three-dimensional competitive systems is investigated. The existence of semi-stable periodic orbits is proved. A generalization of the results of [1–4] is obtained.
Tài liệu tham khảo
Levine, D. S.,Qualitative theory of a third-order nonlinear system with examples in population dynamics and chemical kinetics, Mathematical Biosciences,77(1985), 17–33.
Yuan, Jiancheng,Qualitative analysis of a class of competitive and cooperative systems, Acta Mathematica Sinica, New Series,4:2 (1988), 124–141.
Grassman, W.,Periodic solutions of autonomous differential equations in higher dimensional spaces, Rocky Mountain J. Math.,7(3)(1977), 457–466.
Tang, Baorong,On the existence of periodic solutions in the limited explodator model for the Belousov-Zhabotinskii reaction, Nonlinear Analysis, T. M. A.,13(1989), 1359–1374.
Hirsch, M. W.,Systems of differential equations which are competitive or cooperative. I: Limit sets, SIAM J. Math. Anal.,13(1982), 167–179.
——,Systems of differential equations that are competitive or cooperative. II: Convergence almost everywhere, SIAM J. Math. Anal.,16(1985), 423–429.
——,Systems of differential equations that are competitive or cooperative. III: Competing species, Nonlinearity,1(1988), 51–71.
--,Systems of differential equations that are competitive or cooperative. IV: Structural stability in 3-dimensional systems, SIAM J. Math. Anal., in press.
——,Systems of differential equations that are competitive or cooperative. V: Convergence in 3-dimensional systems, J. Diff. Equats.,80(1989), 94–106.
Smith, H. L.,Systems of ordinary differential equations which generate an order preserving flow. A survey of results, SIAM Rev.,30(1988), 87–113.
——,Periodic orbits of competitive and cooperative systems, J. Diff. Equats.,65(1986), 361–373.
Coppel, W. A., Stability and Asymptotic Behavior of Differential Equations, D. C. Heath, Boston, 1965.
May, R. M. & Leonard, W.J.,Nonlinear aspects of competition between three species, SIAM J. Appl. Math.,29(1975), 243–253.