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We show that this singular set contains interesting information about the dynamical complexity of the model. Firstly, this set can be used as a Poincaré surface for construction of Poincaré sections, and the trajectories then have the recurrence property. We also investigate the distribution of the intersection points. Secondly, the full classification of periodic orbits in the configuration space is performed and existence of UPO is demonstrated. Our general conclusion is that, although the presented model leads to several complications, like divergence of curvature invariants as a measure of sensitive dependence on initial conditions, some global results can be obtained and some additional physical insight is gained from using the conformal Jacobi metric. We also study the complex behavior of trajectories in terms of symbolic dynamics. 相似文献

_{0}<1时,模型只有无病平衡点,运用Jacobi矩阵和Lyapunov泛函得出无病平衡点的全局稳定性;当R

_{0}>1时,无病平衡点不稳定,存在唯一地方病平衡点且是持续的. 相似文献

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*et al*.

*[H. Guo, M. Y. Li and Z. Shuai, Global dynamics of a general class of multistage models for infectious diseases, SIAM J. Appl. Math., 72 (2012), 261–279]*. Under some appropriate and realistic conditions, the global dynamics is completely determined by the basic reproduction number

*R*

_{0}. If

*R*

_{0}≤1, then the infection‐free equilibrium is globally asymptotically stable and the disease dies out in all stages. If

*R*

_{0}>1, then a unique endemic equilibrium exists, and it is globally asymptotically stable, and hence the disease persists in all stages. The results are proved by utilizing the theory of non‐negative matrices, Lyapunov functionals, and the graph‐theoretical approach. Copyright © 2016 John Wiley & Sons, Ltd. 相似文献

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*R*

_{0}. The disease‐free equilibrium is globally asymptotically stable if

*R*

_{0}≤1; when

*R*

_{0}>1, the system is uniformly persistent, and there exists a unique endemic equilibrium that is globally asymptotically. Numerical simulations are conducted to illustrate the theoretical results. 相似文献

*R*

_{0}on WS networks and \(\bar R_0\) on SF networks are obtained respectively. On WS networks, if

*R*

_{0}≤ 1, there is a disease-free equilibrium and it is locally asymptotically stable; if

*R*

_{0}> 1, there is an epidemic equilibrium and it is locally asymptotically stable. On SF networks, if \(\bar R_0 \leqslant 1\), there is a disease-free equilibrium; if \(\bar R_0 > 1\), there is an epidemic equilibrium. Finally, we carry out simulations to verify the conclusions and analyze the effect of the time delay

*τ*, the effective rate λ, average connectivity 〈

*k*〉 and the minimum connectivity m on the epidemic spreading. 相似文献

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