Abstract
Using the continuation theorem of coincidence degree theory and analysis techniques, we establish criteria for the existence of periodic solutions of predator-prey models and impulsive perturbations. It is more appropriate to add the density-dependent term to these models in this paper. Further, computer simulation shows that our models can occur in many forms of complexities including periodic oscillation and gui chaotic strange attractor.
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References
Hofbauer, J., Sigmund, K.: Evolutionary Games and Population Dynamics. Cambridge University, Cambridge (1998)
Meng, X.Z., Chen, L.S.: Permance and global stability in an impulsive LotkaCVolterra N-species competitive system with both discrete delays and continuous delays. Int. J. Biomath. 1, 179–196 (2008)
Jiao, J.J., Chen, L.S.: Global attractivity of a stage-structure variable coefficients predator-prey system with time delay and impulsive perturbations on predators. Int. J. Biomath. 1, 187–208 (2008)
Gaines, R.E., Mawhin, J.L.: Coincidence degree and nonlinear diferential equations. Springer, Berlin (1977)
Hu, D., Zhang, Z.: Four positive periodic solutions to a Lolterra cooperative system with harvesting terms. Nonlinear Analysis: Real World Applications 11, 1115–1121 (2010)
Zhang, J., Gui, Z.J.: Periodic solutions of nonautonomous cellular neural networks with impulses and delays. Nonlinear Analysis: Real World Applications 10, 1891–1903 (2009)
Wei, F.Y., Wang, S.H.: Almost periodic solution and global stability for cooperative L-V diffusion system. Journal of Mathematical Research and Exposition 30, 1108–1116 (2010)
Lin, Z., Liu, J., Pedersen, M.: Periodicity and blowup in a two-species cooperating model. Nonlinar Analysis: Real World Applications 12, 479–486 (2011)
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Yan, Y., Wang, K., Gui, Z. (2011). Existence and Simulations of an Impulsive Appropriate Pest Management SI Model with Biological and Chemical Control. In: Wang, Y., Li, T. (eds) Knowledge Engineering and Management. Advances in Intelligent and Soft Computing, vol 123. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-25661-5_8
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DOI: https://doi.org/10.1007/978-3-642-25661-5_8
Publisher Name: Springer, Berlin, Heidelberg
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