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In this paper, Hopf bifurcation for a delayed SIS epidemic model with stage structure and nonlinear incidence rate is investigated. Through theoretical analysis, we show the positive equilibrium stability and the conditions that Hopf bifurcation occurs. Applying the normal form theory and the center manifold argument, we derive the explicit formulas determining the properties of the bifurcating periodic solutions. In addition, we also study the effect of the inhibition effect on the properties of the bifurcating periodic solutions. To illustrate our theoretical analysis, some numerical simulations are also included. 相似文献
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Pattern formation of a spatial epidemic model with nonlinear incidence rate hI^2 S/(1 + αI^2) is investigated. Our results show that strange spatial dynamics, i.e., filament-like pattern, can be obtained by both mathematical analysis and numerical simulation, which are different from the previous results in the spatial epidemic model such as stripe-like or spotted or coexistence of both pattern and so on. The obtained results well extend the finding of pattern formation in the epidemic model and may well explain the distribution of the infected of some epidemic. 相似文献
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We study the motion of a spiral wave controlled by a local periodic forcing imposed on a region around the spiral tip in an excitable medium. Three types of trajectories of spiral tip are observed: the epicycloid-like meandering, the resonant drift, and the hypocycloid-like meandering. The frequency of the spiral is sensitive to the local periodic forcing. The dependency of spiral frequency on the amplitude and size of local periodic forcing are presented. In addition, we show how the drift speed and direction are adjusted by the amplitude and phase of local periodic forcing, which is consistent with a theoretical analysis based on the weak deformation approximation. 相似文献
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Sun Gui-Quan Wang Shi-Fu Li Ming-Tao Li Li Zhang Juan Zhang Wei Jin Zhen Feng Guo-Lin 《Nonlinear dynamics》2020,101(3):1981-1993
Nonlinear Dynamics - Due to the strong infectivity of COVID-19, it spread all over the world in about three months and thus has been studied from different aspects including its source of... 相似文献
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This paper considers the Holling-Tanner model for predator-prey with self and cross-diffusion. From the Turing theory, it is believed that there is no Turing pattern formation for the equal self-diffusion coefficients. However, combined with cross-diffusion, it shows that the system will exhibit spotted pattern by both mathematical analysis and numerical simulations. Furthermore, asynchrony of the predator and the prey in the space. The obtained results show that cross-diffusion plays an important role on the pattern formation of the predator-prey system. 相似文献
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An SIS network model incorporating the influence of media coverage on transmission rate is formulated and analyzed. We calculate the basic reproduction number R0 by utilizing the local stability of the disease-free equilibrium. Our results show that the disease-free equilibrium is globally asymptotically stable and that the disease dies out if R0 is below 1; otherwise, the disease will persist and converge to a unique positive stationary state. This result may suggest effective control strategies to prevent disease through media coverage and education activities in finite-size scale-free networks. Numerical simulations are also performed to illustrate our results and to give more insights into the dynamical process. 相似文献
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In this paper, pattern formation of a predator-prey model with spatial effect is investigated. We obtain the conditions for
Hopf bifurcation and Turing bifurcation by mathematical analysis. When the values of the parameters can ensure a stable limit
cycle of the no-spatial model, our study shows that the spatially extended models have spiral waves dynamics. Moreover, the
stability of the spiral wave is given by the theory of essential spectrum. Furthermore, although the environment is heterogeneous,
the system still exhibit spiral waves. The obtained results confirm that diffusion can form the population in the stable motion,
which well enrich the finding of spatiotemporal dynamics in the predator-prey interactions and may well explain the field
observed in some areas. 相似文献