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    Relaxation Oscillation in SEIR Epidemic Models with the Intrinsic Growth Rate by Yingying Zhang, Ruohan Wang, Yanan Cai

    Published 2024-01-01
    “…By utilizing the singular perturbation theory and center manifold theorem, we extend the relaxation oscillation of three-dimensional SIR models to the four-dimensional SEIR models and prove the existence of stable relaxation oscillation with a large amplitude in the model. …”
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    Hopf bifurcation analysis in a diffusive predator-prey system with delay and surplus killing effect by Zuolin Shen, Junjie Wei

    Published 2018-05-01
    “…Furthermore, an algorithm for determining the direction of Hopf bifurcation and stability of bifurcating periodic solutions is derived by using the theory of normal form and center manifold. Finally, some numerical simulations are presented to illustrate the analytical results obtained.…”
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    Hopf Bifurcation and Global Periodic Solutions in a Predator-Prey System with Michaelis-Menten Type Functional Response and Two Delays by Yunxian Dai, Yiping Lin, Huitao Zhao

    Published 2014-01-01
    “…We focus on the case with two unequal and non-zero delays present in the model, study the local stability of the equilibria and the existence of Hopf bifurcation, and then obtain explicit formulas to determine the properties of Hopf bifurcation by using the normal form method and center manifold theorem. Special attention is paid to the global continuation of local Hopf bifurcation when the delays τ1≠τ2.…”
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