Hybrid control of Hopf bifurcation in complex networks with delays

Cheng, Zunshui; Cao, Jinde

doi:10.1016/j.neucom.2013.10.028

Cited by 37 publications

(26 citation statements)

References 17 publications

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“…From an ecological viewpoint, the interaction parameter areas of coexistence for two components are desirable. This method is important for understanding the regulatory chemical mechanisms of ecological systems, which provides a control mechanism to ensure a coexistence transition from an equilibrium to a periodic oscillation with desired amplitude and robust period [2,5,15,16,22,23,26]. In addition, we would like to point out that we can also investigate the Hopf bifurcation of system (1.3) by choosing the delay τ 2 as bifurcation parameter.…”

Section: Discussionmentioning

confidence: 99%

Time effect on the dynamical behavior of a life energy system dynamic model

Xu¹,

Li²

2017

J. Nonlinear Sci. Appl.

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This article is concerned with a life energy system dynamic model with two different delays. A set of sufficient criteria which ensures the local stability and the existence of Hopf bifurcation for the model is derived. Some explicit formulas which determine the nature of Hopf bifurcations are obtained by means of the normal form theory and center manifold theorem. Our analytical findings are supported by numerical experiments. Finally, a brief conclusion is included.

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Section: Discussionmentioning

confidence: 99%

Time effect on the dynamical behavior of a life energy system dynamic model

Xu¹,

Li²

2017

J. Nonlinear Sci. Appl.

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“…Especially, the hybrid control has also been widely used recently. Cheng and Cao [20] considered Hopf bifurcation control for a complex network model with time delays, and they presented a hybrid control strategy to control the model. Kiani et al [21] used the hybrid control method for a three-pole active magnetic bearing (AMB), and the method showed that the power usage decreased in the hybrid control method comparing to a simple linear control.…”

Section: Mathematical Problems In Engineeringmentioning

confidence: 99%

Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response

Peng

Zhang

Lim

et al. 2018

Mathematical Problems in Engineering

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Hopf bifurcation analysis of a delayed ecoepidemiological model with nonlinear incidence rate and Holling type II functional response is investigated. By analyzing the corresponding characteristic equations, the conditions for the stability and existence of Hopf bifurcation for the system are obtained. In addition, a hybrid control strategy is proposed to postpone the onset of an inherent bifurcation of the system. By utilizing normal form method and center manifold theorem, the explicit formulas that determine the direction of Hopf bifurcation and the stability of bifurcating period solutions of the controlled system are derived. Finally, some numerical simulation examples confirm that the hybrid controller is efficient in controlling Hopf bifurcation.

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“…For the uncontrolled model (32), we can easily obtain V * = 0.815 and τ 0 = 0.6349. From Theorem 1 and Remark 8, model (32) is locally asymptotically stable at the equilibrium point when τ = 0.6 < τ 0 , which is illustrated in Fig. 1, and a Hopf bifurcation occurs when τ = 0.65 > τ 0 , as shown in Fig.…”

Section: Stability and Direction Of Bifurcating Periodic Solutionsmentioning

confidence: 99%

“…When k p = 2, k i = 0 and k d = À 10, controller (2) is a PD controller. The PD controller is used to control model (32) with τ = 0.2. The controlled model has two equilibria 0.815 and 0.505.…”

Section: Remark 12mentioning

confidence: 99%

Bifurcation control of small‐world networks with delays VIA PID controller

Tao

Xiao

Jiang

et al. 2018

Asian Journal of Control

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In this paper, the problem of bifurcation control for a small‐world network model with time delay is studied. We first put forward a Proportional‐Integral‐Derivative (PID) feedback scheme to control the Hopf bifurcation of the network. The time delay is selected as the bifurcation parameter. The conditions of the stability and Hopf bifurcation are given for the controlled network. By using the center manifold theorem and the normal form theory, the direction and stability of bifurcating periodic solutions are confirmed. The feasible region of the parameters of the controller is determined. It is found that the bifurcation dynamics of the small‐world network are optimized by adjusting the parameters of the PID controller. Finally, a numerical example verifies the effectiveness of the designed PID controller, and the relationships between the onset of the Hopf bifurcation and the control parameters are obtained.

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Hybrid control of Hopf bifurcation in complex networks with delays

Cited by 37 publications

References 17 publications

Time effect on the dynamical behavior of a life energy system dynamic model

Time effect on the dynamical behavior of a life energy system dynamic model

Hopf Bifurcation and Hybrid Control of a Delayed Ecoepidemiological Model with Nonlinear Incidence Rate and Holling Type II Functional Response

Bifurcation control of small‐world networks with delays VIA PID controller

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