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In this paper, we study a class of SIR model with time-delay and evolutionary effects under the homogeneous Neumann boundary conditions. Firstly, the stability of the positive equilibrium point is analyzed with time delay as the parameter, and the existence condition of Hopf bifurcation is given. Secondly, the bifurcation direction and the stability of periodic solutions are given by using the theory of normal form and center manifold. Finally, Matlab was used for the numerical simulation to verify the correctness of the conclusion, and it is concluded that the time delay will make the stable system become unstable and generate Hopf bifurcation. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Zhejiang University (Science Edition) is the property of Journal of Zhejiang University (Science Edition) Editorial Office and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Control Theory & Applications / Kongzhi Lilun Yu Yinyong is the property of Editorial Department of Control Theory & Applications and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Chongqing University of Technology (Natural Science) is the property of Chongqing University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

The paper formulates a SEIR model with time delay effect to explain the influence of media reports on diseases. Firstly, the basic reproduction number of the model is determined by the method of next generation matrix. The existence and the global stability of the equilibrium point are discussed. Secondly, sufficient conditions of Hopf bifurcation of the model are given. Finally, by numerical simulation, we prove the correctness of the theories. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Central China Normal University is the property of Huazhong Normal University and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Henan University of Science & Technology, Natural Science is the property of Editorial Office of Journal of Henan University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In this paper we establish a predator-prey model with a protection area and a open habitat for prey.Additive Allee effect in the prey of protection area and the environment carrying capacity of prey are considered.According to the biology of predator-prey system,fast and slow time scales are considered in some of the parameters.Based on two different time scales,the system is divided into a fast and a slow system.We analyze the dynamics of the slow system.Existence and global stability of equilibriums,existence of Hopf bifurcation and the limit cycle are performed.Combining mathematica analysis and numerical simulation,we verified the results above.The results show that the Allee effect change the conditions of the two species coexist.It makes the system dynamic behavior more complicated. [ABSTRACT FROM AUTHOR]

Copyright of Chinese Journal of Computational Mechanics / Jisuan Lixue Xuebao is the property of Chinese Journal of Computational Mechanics Editorial Office, Dalian University of Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Ring structures are widely used in neural networks,and previous research with respect to neural dynamic bifurcation were confined to models with single-ring structure.Notably,neural networks are composed of thousands of neurons coupled together,and these structures are so complex that they cannot be accurately described through only a single-ring structure,and therefore is more practical for investigating neural network models with multiple ring topology.In this paper,an asymmetric model with double-ring neural structure is proposed,and the stability and Hopf bifurcation of the model are investigated.Numerical simulations are subsequently actualized to corroborate the theoretical results. [ABSTRACT FROM AUTHOR]

Copyright of Journal of Guangxi Normal University - Natural Science Edition is the property of Gai Kan Bian Wei Hui and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of Journal of Harbin University of Science & Technology is the property of Journal of Harbin University of Science & Technology and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Copyright of China Sciencepaper is the property of China Sciencepaper and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

In order to maintain the harmony and stability of ecosystems, in this paper, the stability of Nicholson's blowflies model with time delay was investigated. The distribution of the characteristic roots, the stability of the equilibrium, the existence of Hopf bifurcation and its conditions were discussed. Meanwhile, some simulations were carried out, which supported the theoretical results obtained previously and the global existence of Hopf bifurcation near the positive equilibrium point was got. At last, the reasons of circulating ecosystems were explained by the bifurcation theory. [ABSTRACT FROM AUTHOR]

In this paper, delay dynamics of a worm propagation model has been investigated with different incidence rates in wireless sensor network. Processing time delay occurs in the proposed model due to time consumed during monitoring the erratic behaviors of the nodes and isolating it from the network. Sufficient conditions for the existence of equilibrium points, stability analysis and Hopf bifurcation of the system are derived by analyzing distribution of roots of an associated characteristic equation. Global stability for worm-induced equilibrium is derived by constructing a suitable Lyapunov function. To verify analytical results, numerical simulations are carried out. In the case that the processing time delay exceeds the critical value, the worms in the network is beyond the control. There are many significant features of wireless sensor networks, among them coverage area is the most effective factor with respect to worm control and security purposes. The value of some influential parameters of sensor network are carefully selected so that the oscillations can be reduced and removed from the network. According to comparative study of model systems, it can be concluded that the incidence rate is one of the best selection for worm control and security purposes in wireless sensor network.

Copyright of Applied Mathematics & Mechanics (1000-0887) is the property of Applied Mathematics & Mechanics and its content may not be copied or emailed to multiple sites or posted to a listserv without the copyright holder's express written permission. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

This paper is devoted to Hopf bifurcation of a delayed SVEIR model with partial immunization that describes worms propagation on internet. Sufficient conditions for existence of Hopf bifurcation are obtained by considering the latent period time delay of worms as the bifurcation parameter. Properties of Hopf bifurcation are then investigated with the help of the normal form theory and the center manifold theorem. Numerical simulations show that worms propagation in internet can be controlled and eliminated by shortening the time delay.

This paper is concerned with a three-component model consisting of two prey and one predator with time delay and the inclusion of Holling type-Ⅱ response function incorporating a constant proportion of prey refuge. It is shown that the positive equilibrium of the system is locally asymptotically stable when the time delay is small enough. Changes of stability of the positive equilibrium will cause bifurcating periodic solutions as the time delay passes through a critical value. Particularly, the direction of Hopf bifurcation and the stability of the periodic solutions are determined by using the normal form method and center manifold theorem. Finally, the numerical simulations are carried out to verify our theoretical findings.