Hopf bifurcation for simple food chain model with delay.
Cavani, Mario, Lara, Teodoro, Romero, Sael (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Cavani, Mario, Lara, Teodoro, Romero, Sael (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Abbas, Syed, Banerjee, Malay (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Yafia, Radouane (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Zaman, Gul (2011)
Bulletin of the Malaysian Mathematical Sciences Society. Second Series
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Brauer, Fred (2005)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Zhang, Xiao, Xu, Rui, Gan, Qintao (2009)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Zhang, Jin-Zhu, Jin, Zhen, Liu, Quan-Xing, Zhang, Zhi-Yu (2008)
Discrete Dynamics in Nature and Society
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Eberl, Hermann J., Frederick, Mallory R., Kevan, Peter G. (2010)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Q. J. A. Khan, E. V. Krishnan (2003)
Applications of Mathematics
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We study a mathematical model which was originally suggested by Greenhalgh and Das and takes into account the delay in the recruitment of infected persons. The stability of the equilibria are also discussed. In addition, we show that the introduction of a time delay in the transmission term can destabilize the system and periodic solutions can arise by Hopf bifurcation.
Marik, Robert, Pribylova, Lenka (2006)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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Gaff, Holly D., Hartley, David M., Leahy, Nicole P. (2007)
Electronic Journal of Differential Equations (EJDE) [electronic only]
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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...