Commenced in January 2007
Frequency: Monthly
Edition: International
Paper Count: 31821
Periodic Solutions for a Two-prey One-predator System on Time Scales

Authors: Changjin Xu


In this paper, using the Gaines and Mawhin,s continuation theorem of coincidence degree theory on time scales, the existence of periodic solutions for a two-prey one-predator system is studied. Some sufficient conditions for the existence of positive periodic solutions are obtained. The results provide unified existence theorems of periodic solution for the continuous differential equations and discrete difference equations.

Keywords: Time scales, competitive system, periodic solution, coincidence degree, topological degree.

Digital Object Identifier (DOI):

Procedia APA BibTeX Chicago EndNote Harvard JSON MLA RIS XML ISO 690 PDF Downloads 1230


[1] M. Bohner and A Peterson, Dynamic Equations on Times Scales: An Introduction with Applications. Boston: Birkh¨a user, 2001.
[2] M. Bohner and A Peterson, Advances in Dynamic Equations on Time Scales. Boston: Birkh¨a user, 2003.
[3] S. Hilger, Analysis on measure chains-a unfified approach to continuous and discrete calculus. Results in Math. 18 (1990) 18-56.
[4] E. R. Kaufmann and Y. N. Raffoul, Periodic solutions for a neutral nonlinear dynamical equation on a time scale. J. Math. Anal. Appl. 319 (1) (2006) 315-325.
[5] Y. K. Li and H. T. Zhang, Existence of periodic solutions for a periodic mutualism model on time scales, J. Math. Anal. Appl. 343(2) (2008) 818-825.
[6] M. Fazly and M. Hesaaraki, Periodic solutions for predator-prey systems with Beddington-DeAngelis functional response on time scales. Nonlinear Anal.: Real World Appl. 9(3) (2008) 1224-1235.
[7] H. J. Li, A. P. Liu and Z. T. Hao, Existence for periodic solutions of a ratio-dependent predator-prey system with time-varying delays on time scales. Anal. Appl. 8(3) (2010) 227-233.
[8] W. P. Zhang, P. Bi and D. M. Zhu, Periodicity in a ratio-dependent predator-prey system with stage-structured predator on time scales. Nonlinear Anal.: Real World Appl. 9(2) (2008) 344-353.
[9] J. Liu, Y. K. Li and L. L. Zhao, On a periodic solution predator-prey system with time delays on time scales. Commun. Nonlinear Sci. Numer. Simulat. 14(8) (2009) 3432-3438.
[10] H. Baek, Species extiction and permanence of an impulsively controlled two-prey one-predator system with seasonal effects. BioSystems 98(1) (2009) 7-18.
[11] B. Aulbach and S. Hilger, Linear Dynamical Processes with Inhomogeneous Time Scales, Nonlinear Dynamics and Quantum Dynamical Systems. Berlin: Akademie Verlage, 1990.
[12] V. Lakshmikantham, S. Sivasundaram and B. Kaymarkcalan, Dynamic Systems on Measure Chains. Boston: Kluwer Academic Publishers, 1996.
[13] R. E. Gaines and J. L. Mawhin, Coincidence Degree and Nonlinear Differential Equations. Berlin: Springer-verlag, 1997.