Controlling chaos in Internet congestion control model

Chen, Liang; Wang, Xiaofan; Han, Zhanghua

doi:10.1016/j.chaos.2003.09.037

Cited by 36 publications

(13 citation statements)

References 22 publications

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“…It is well known that stabilization and chaotification are two main problems in this field [8][9][10]. The task of purposely creating chaos, called chaotification or anticontrol of chaos, has great potential in nontraditional applications such as those found within the contexts of physical, chemical, mechanical, electrical, optical, and particularly biological and medical systems [11].…”

Section: Introductionmentioning

confidence: 99%

Chaotification of nonlinear discrete systems via immersion and invariance

et al. 2010

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This paper is concerned with the chaotification of nonlinear discrete systems. A novel method based on (system) immersion and (manifold) invariance (I&I) is introduced to chaotify nonlinear discrete systems. Its basic idea is to immerse an ideal system which holds chaotic properties and may be a lower dimension into the plant system, and then control trajectories of the plant system to converge toward the invariant manifold where the ideal system is immersed. For a class of linearizable systems, we present the immersion and the control law such that these systems can be chaotified through I&I design. An illustrative example with simulation is presented to validate the proposed chaotification scheme.

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Section: Introductionmentioning

confidence: 99%

Chaotification of nonlinear discrete systems via immersion and invariance

et al. 2010

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“…This field also begins to draw much attention from researchers. In [11], the authors have proposed that AQM/TCP can be modeled as a discretetime dynamical system, which may create complex bifurcating and chaotic behavior. The results in [12][13][14] have also shown the occurrence of a Hopf bifurcation in a rate control algorithm with a single link and source.…”

Section: Introductionmentioning

confidence: 99%

Hopf and resonant double Hopf bifurcation in congestion control algorithm with heterogeneous delays

2010

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The congestion control algorithm, which has dynamic adaptations at both user ends and link ends, with heterogeneous delays is considered and analyzed. Some general stability criteria involving the delays and the system parameters are derived by generalized Nyquist criteria. Furthermore, by choosing one of the delays as the bifurcation parameter, and when the delay exceeds a critical value, a limit cycle emerges via a Hopf bifurcation. Resonant double Hopf bifurcation is also found to occur in this model. An efficient perturbation-incremental method is presented to study the delay-induced resonant double Hopf bifurcation. For the bifurcation parameter close to a double Hopf point, the approximate expressions of the periodic solutions are updated iteratively by use of the perturbation-incremental method. Simulation results have verified and demonstrated the correctness of the theoretical results.

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“…The past two decades has witnessed significant progress on chaotic systems [1,2] because of its potential applications in secure communication, neural networks [3][4][5][6][7], biological networks, etc. Since Pecora and Carroll [8] synchronizing two identical chaotic systems with different initial conditions, a number of approaches have been proposed to achieve chaos synchronization such as PC method [8], OGY method [9], nonlinear control [10], adaptive method [11], impulsive control [12], and coupling control [13], etc.…”

Section: Introductionmentioning

confidence: 99%