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Existence and global attractivity of positive periodic solution to a Lotka-Volterra model. (English) Zbl 1205.34058
Summary: By using Mawhin’s continuation theorem and constructing a suitable Lyapunov functional, a Lotka-Volterra model with mutual interference and Holling III type functional response is studied. Some sufficient conditions are obtained for the existence, uniqueness and global attractivity of a positive periodic solution of the model. Furthermore, the conditions are related to the interference constant $m$.

MSC:
34C60Qualitative investigation and simulation of models (ODE)
34C05Location of integral curves, singular points, limit cycles (ODE)
92D25Population dynamics (general)
34D20Stability of ODE
47N20Applications of operator theory to differential and integral equations
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References:
[1] Teng, Z. D.: On the persistence and positive periodic solution for planar competing Lotka--Volterra systems. Ann. differential equations 3, No. 3, 275-286 (1997) · Zbl 0887.34038
[2] Teng, Z. D.; Chen, L. S.: Necessary and sufficient conditions for existence of positive periodic solutions of periodic predator--prey systems. Acta math. Sci. 18, No. 4, 402-406 (1998) · Zbl 0914.92019
[3] Chen, C.; Chen, F. D.: Conditions for global attractivity of a multispecies ecological competition--predator system with a Holling III type functional response. J. biomath. 19, No. 2, 136-140 (2004)
[4] Chen, F. D.: The permanence and global attractivity of Lotka--Volterra competition system with feedback controls. Nonlinear anal. RWA 7, 133-143 (2006) · Zbl 1103.34038
[5] Hassel, M. P.: Density dependence in single-species population. J. anim. Ecol. 44, 283-295 (1975)
[6] Chen, L. S.: Mathematical ecology modelling and research methods. (1988)
[7] Wang, K.; Zhu, Y. L.: Global attractivity of positive periodic solution for a Volterra model. Appl. math. Comput. 203, 493-501 (2008) · Zbl 1178.34052
[8] Gaines, R. E.; Mawhin, J. L.: Coincidence degree and nonlinear differential equations. (1977) · Zbl 0339.47031
[9] Gopalasamy, K.: Stability and oscillation in delay equation of population dynamics. (1992)