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Stability Analysis of P2P Worm Propagation Model with Dynamic Quarantine Defense  [cached]
Wei Yang,Gui-RAN Chang,Yu Yao,Xiao-meng Shen
Journal of Networks , 2011, DOI: 10.4304/jnw.6.1.153-162
Abstract: The propagation of P2P worm covers large area and causes great damage. A dynamic quarantine protocol is designed to quarantine the suspicious host in the P2P system. Then a mathematical model of PWPQ is proposed which considering the dynamic process of peer joining and leaving. The effect of dynamic quarantine on active P2P worm is analyzed. Through stability analysis for PWPQ model, a key argument of infection-free stable point which affect the P2P worm propagation, the basic reproduction number, is deduced. Simulation results show that the propagation model of P2P worms can reflect the P2P worm behaviors and the performance of our model is significantly better than other models, in terms of decreasing the number of infected hosts and reducing the worm propagation speed. When the basic reproduction number is less than 1, infection-free stable point is global stability and the P2P worm are eliminated. The PWPQ model gives some way to control P2P worm break out and gives guidelines to P2P worm detection and defense.
Worm propagation modeling and analysis based on quarantine

LI Tao,GUAN Zhi-hong,

计算机应用研究 , 2008,
Abstract: This paper presented a worm propagation model with quarantine strategy based on the classical epidemic Kermack-McKendrick model.Established the conditions and threshold to the existence of various equilibriums.By means of linearization and constructing Liapunov functional,obtained the conditions about the globally asymptotic stability.The analysis shows that the model can efficiently prevent worms' propagation.Numerical simulations confirmed our theoretical results.
Worm Propagation Modeling and Analysis Based on Quarantine

ZHANG Yun-Kai,WANG Fang-Wei,MA Jian-Feng,ZHANG Yu-Qing Computer Science,Technology,Xidian University,Xi'an Network Center,Hebei Normal University,Shijiazhuang National Computer Network Intrusion Protection Center,GSCAS,Beijing,

计算机科学 , 2005,
Abstract: In recent years,the worms that had a dramatic increase in. the frequency and virulence of such outbreaks have become one of the major threats to the security of the Internet. In this paper,we provide a worm propagating model. It bases on the classical epidemic Kermack-Kermack model,adopts dynamic quarantine strategy, dynamic in- fecting rate and removing rate. The analysis shows that model can efficiently reduce a worm's propagation speed, which can give us more precious time to defend it,and reduce the negative influence of worms. The simulation results verify the effectiveness of the model.
Nonstandard Hopf bifurcation in switched  [PDF]
Xiao-Song Yang,Songmei Huan
Mathematics , 2010,
Abstract: This paper presents an analysis on nonstandard generalized Hopf bifurcation in a class of switched systems where the lost of stability of linearized systems is not due to the crossing of their complex conjugate eigenvalues but relevant to the switching laws between the subslystems. Thus is remarkably different from the mechanism of the Hopf bifurcation and the generalized Hopf bifurcation studied in the literature.
The Hopf bifurcation with bounded noise  [PDF]
Ryan Botts,Ale Jan Homburg,Todd Young
Mathematics , 2011,
Abstract: We study Hopf-Andronov bifurcations in a class of random differential equations (RDEs) with bounded noise. We observe that when an ordinary differential equation that undergoes a Hopf bifurcation is subjected to bounded noise then the bifurcation that occurs involves a discontinuous change in the Minimal Forward Invariant set.
Unfoldings of singular Hopf bifurcation  [PDF]
John Guckenheimer,Philipp Meerkamp
Mathematics , 2011,
Abstract: Singular Hopf bifurcation occurs in generic families of vector-fields with two slow variables and one fast variable. Normal forms for this bifurcation depend upon several parameters, and the dynamics displayed by the normal forms is intricate. This paper analyzes a normal form for this bifurcation. It presents extensive diagrams of bifurcations of equilibrium points and periodic orbits that are close to singular Hopf bifurcation. In addition, parameters are determined where there is a tangency between invariant manifolds that are important in the appearance of mixed-mode oscillations in systems near singular Hopf bifurcation. One parameter of the normal form is identified as the primary bifurcation parameter, and the paper presents a catalog of bifurcation sequences that occur as the primary bifurcation parameter is varied. These results are applied to estimate the parameters for the onset of mixed-mode oscillations in a model of chemical oscillations.
Hamiltonian Hopf bifurcation with symmetry  [PDF]
Pascal Chossat,Juan-Pablo Ortega,Tudor S. Ratiu
Mathematics , 2001, DOI: 10.1007/s002050200182
Abstract: In this paper we study the appearance of branches of relative periodic orbits in Hamiltonian Hopf bifurcation processes in the presence of compact symmetry groups that do not generically exist in the dissipative framework. The theoretical study is illustrated with several examples.
Uncertainty Transformation via Hopf Bifurcation in Fast-Slow Systems  [PDF]
Christian Kuehn
Mathematics , 2015,
Abstract: Propagation of uncertainty in dynamical systems is a significant challenge. Here we focus on random multiscale ordinary differential equation models. In particular, we study Hopf bifurcation in the fast subsystem for random initial conditions. We show that a random initial condition distribution can be transformed during the passage near a delayed/dynamic Hopf bifurcation: (I) to certain classes of symmetric copies, (II) to an almost deterministic output, (III) to a mixture distribution with differing moments, and (IV) to a very restricted class of general distributions. We prove under which conditions the cases (I)-(IV) occur in certain classes vector fields.
Noise induced Hopf bifurcation  [PDF]
I A Shuda,S S Borysov,A I Olemskoi
Physics , 2008,
Abstract: We consider effect of stochastic sources upon self-organization process being initiated with creation of the limit cycle induced by the Hopf bifurcation. General relations obtained are applied to the stochastic Lorenz system to show that departure from equilibrium steady state can destroy the limit cycle in dependence of relation between characteristic scales of temporal variation of principle variables. Noise induced resonance related to the limit cycle is found to appear if the fastest variations displays a principle variable, which is coupled with two different degrees of freedom or more.
Fractal analysis of Hopf bifurcation at infinity  [PDF]
Goran Radunovi?,Vesna ?upanovi?,Darko ?ubrini?
Mathematics , 2015, DOI: 10.1142/S0218127412300431
Abstract: Using geometric inversion with respect to the origin we extend the definition of box dimension to the case of unbounded subsets of Euclidean spaces. Alternative but equivalent definition is provided using stereographic projection on the Riemann sphere. We study its basic properties, and apply it to the study of the Hopf-Takens bifurcation at infinity.
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