State feedback control at Hopf bifurcation in an exponential RED algorithm model

Xiao, Min; Jiang, Guoping; Zhao, Lindu

doi:10.1007/s11071-013-1221-0

Cited by 26 publications

(3 citation statements)

References 33 publications

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“…Stability and bifurcation are important issues in the research of fractional-order differential equation models. Hopf bifurcation is widely focused on because it reflects the properties of periodic solutions near the steady-state of nonlinear systems [28][29][30][31]. However, the appearance of Hopf bifurcation is also a sign that the system appears periodic oscillation and enters an unstable state from a stable state.…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Control of a Fractional-Order Delay Stage Structure Prey-Predator Model with Two Fear Effects and Prey Refuge

2022

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A generalized delay stage structure prey-predator model with fear effect and prey refuge is considered in this paper via introducing fractional-order and fear effect induced by immature predators. Hopf bifurcation and control of this system are investigated though regarding the delay as the parameter. Firstly, by using the method of linearization and Laplace transform, the roots of the characteristic equation of the linearized system of the original system are discussed, and the sufficient conditions for the system exhibits an unstable state of symmetrical periodic oscillation (Hopf bifurcation) are explored. Secondly, a linear delay feedback controller is added to the system to increase the stability domain successfully. Thirdly, numerical simulations are performed to validate the theoretical analysis, and the various impacts on the dynamical behavior of the system occurring by fear effects, prey refuge, and each fractional-order are illustrated, respectively. Furthermore, the influence of feedback gain on the bifurcation critical point is analyzed. Finally, an analysis based on the results and in-depth research about this system under the biological background is stated in the conclusion.

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Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Control of a Fractional-Order Delay Stage Structure Prey-Predator Model with Two Fear Effects and Prey Refuge

2022

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“…In recent years, the stability analysis and the feedback control of time delay systems have been widely investigated since delays are often encountered in various engineering systems (see, i.e., [29][30][31][32][33][34][35]). On the other hand, descriptor systems with or without time delay have been extensively studied in recent years (see, i.e., [11,14,[17][18][19][20][21][22][23][24]27], and the references therein).…”

Section: Introductionmentioning

confidence: 99%

Local stability and Hopf bifurcation of two-dimensional nonlinear descriptor system

Liao

Xie

2015

Nonlinear Dyn

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Descriptor systems, which are also called differential-algebraic systems, singular systems, degenerate systems, constrained systems and so on, have been one of the major research topics in engineering field. However, problems related to the local stability and the Hopf bifurcation of nonlinear descriptor systems with time delay have not been thoroughly investigated. In this paper, we consider the dynamical behavior of twodimensional nonlinear descriptor systems with time delay. First, local stability of the system is analyzed using the location of the roots of the characteristic equation of the corresponding linearized system. It is well known that the equilibrium of the linearized system is locally asymptotically stable if all roots of the corresponding characteristic equation locate in the left half of the complex plane, and they are uniformly bounded away from the imaginary axis. Otherwise, the equilibrium is unstable. The conditions for the existence of Hopf bifurcation are investigated in detail by using the time delay as a bifurcation parameter. Furthermore, based on the descriptor and the "neutral-type" model transformation, some special neutral differential equations can be equivalently transformed into the nonlinear descriptor systems. Finally, the correctness and the effectiveness of the theoretical analysis are justified by numerical examples.

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“…It is worth to point out that recent many works have been done for wired access network. For details, we refer to [13][14][15][16].…”

Section: Introductionmentioning

confidence: 99%

Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network

Zhao

Sun

Huicheng

2014

Abstract and Applied Analysis

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We drive a scalar delay differential system to model the congestion of a wireless access network setting. The Hopf bifurcation of this system is investigated using the control and bifurcation theory; it is proved that there exists a critical value of delay for the stability. When the delay value passes through the critical value, the system loses its stability and a Hopf bifurcation occurs. Furthermore, the direction and stability of the bifurcating periodic solutions are derived by applying the normal form theory and the center manifold theorem. Finally, some examples and numerical simulations are presented to show the feasibility of the theoretical results.

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State feedback control at Hopf bifurcation in an exponential RED algorithm model

Cited by 26 publications

References 33 publications

Hopf Bifurcation and Control of a Fractional-Order Delay Stage Structure Prey-Predator Model with Two Fear Effects and Prey Refuge

Hopf Bifurcation and Control of a Fractional-Order Delay Stage Structure Prey-Predator Model with Two Fear Effects and Prey Refuge

Local stability and Hopf bifurcation of two-dimensional nonlinear descriptor system

Hopf Bifurcation and Stability Analysis of a Congestion Control Model with Delay in Wireless Access Network

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