Dynamical systems modelling of the interactions of animal stocking density and soil fertility in grazed pasture.
Wickham, I.D., Wake, G.C., Woodward, S.J.R., Thorrold, B.S. (1997)
Journal of Applied Mathematics and Decision Sciences
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Wickham, I.D., Wake, G.C., Woodward, S.J.R., Thorrold, B.S. (1997)
Journal of Applied Mathematics and Decision Sciences
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Udwadia, Firdaus, Leitmann, George, Lambertini, Luca (2006)
Discrete Dynamics in Nature and Society
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Faria, João Ricardo, León-Ledesma, Miguel A. (2008)
Discrete Dynamics in Nature and Society
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Huo, Hai-Feng, Dang, Shuai-Jun, Li, Yu-Ning (2010)
Abstract and Applied Analysis
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Soewono, Edy, Supriatna, Asep K. (2001)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Piqueira, José Roberto C. (2010)
Mathematical Problems in Engineering
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Wang, Wenjuan, Xin, Jingqi, Zhang, Fengqin (2010)
Discrete Dynamics in Nature and Society
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Sanyi Tang (2003)
ESAIM: Mathematical Modelling and Numerical Analysis - Modélisation Mathématique et Analyse Numérique
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In this paper, the main purpose is to reveal what kind of qualitative dynamical changes a continuous age-structured model may undergo as continuous reproduction is replaced with an annual birth pulse. Using the discrete dynamical system determined by the stroboscopic map we obtain an exact periodic solution of system with density-dependent fertility and obtain the threshold conditions for its stability. We also present formal proofs of the supercritical flip bifurcation at the bifurcation...
Corbett, B.D., Moghadas, S.M., Gumel, A.B. (2003)
International Journal of Mathematics and Mathematical Sciences
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Tumwiine, J., Mugisha, J.Y.T., Luboobi, L.S. (2007)
Computational & Mathematical Methods in Medicine
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Tian, Xiaohong, Xu, Rui (2009)
Discrete Dynamics in Nature and Society
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Liu, Rongsong, Wu, Jianhong, Zhu, Huaiping (2007)
Computational & Mathematical Methods in Medicine
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Shu Liao, Weiming Yang (2013)
International Journal of Applied Mathematics and Computer Science
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In this paper, we present a vaccination model with multiple transmission ways and derive the control reproduction number. The stability analysis of both the disease-free and endemic equilibria is carried out, and bifurcation theory is applied to explore a variety of dynamics of this model. In addition, we present numerical simulations to verify the model predictions. Mathematical results suggest that vaccination is helpful for disease control by decreasing the control reproduction number...