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Mechanism analysis of regulating Turing instability and hopf bifurcation of malware propagation in mobile wireless sensor networks

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Chinese Physics B 2024年第6期33卷 125-140页

作者：黄习习肖敏 Leszek Rutkowski 包海波黄霞曹进德 College of Automation&College of Artificial Intelligence Nanjing University of Posts and TelecommunicationsNanjing 210023China Systems Research Institute of the Polish Academy of Sciences 01-447 WarsawPoland College of Electrical Engineering and Automation Shandong University of Science and TechnologyQingdao 266590China School of Mathematics Southeast UniversityNanjing 210096China

A dynamical model is constructed to depict the spatial-temporal evolution of malware in mobile wireless sensor networks(MWSNs). Based on such a model, we design a hybrid control scheme combining parameter perturbation and state feedback to effectively manipulate the spatiotemporal dynamics of malware propagation. The hybrid control can not only suppress the Turing instability caused by diffusion factor but can also adjust the occurrence of hopf bifurcation induced by time delay. Numerical simulation results show that the hybrid control strategy can efficiently manipulate the transmission dynamics to achieve our expected desired properties, thus reducing the harm of malware propagation to MWSNs.

关键词： mobile wireless sensor networks reaction-diffusion hopf bifurcation hybrid control

hopf bifurcation ANALYSIS IN A 4D-HYPERCHAOTIC SYSTEM

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Journal of Systems Science & Complexity 2010年第4期23卷 748-758页

作者： Kangming ZHANG Qigui YANG School of Mathematical Sciences South China University of Technology Guangzhou 510640 China Department of Science and Arts Nanehang Academy of Army Nanehang 330013 China

This paper investigates the hopf bifurcation of a 4-dimensional hyperchaotic system withonly one equilibrium.A detailed set of conditions are derived,which guarantee the existence of thehopf ***,the standard normal form theory is applied to determine the directionand type of the hopf bifurcation,and the approximate expressions of bifurcating periodic solutions andtheir *** addition,numerical simulations are used to justify theoretical results.

关键词： Chaos hopf bifurcation hyperchaos normal form stability.

hopf bifurcation analysis of Chen circuit with direct time delay feedback

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Chinese Physics B 2010年第3期19卷 164-175页

作者：任海鹏李文超刘丁 School of Automation and Information Engineering Xi'an University of Technology

Direct time delay feedback can make non-chaotic Chen circuit chaotic. The chaotic Chen circuit with direct time delay feedback possesses rich and complex dynamical behaviours. To reach a deep and clear understanding of the dynamics of such circuits described by delay differential equations, hopf bifurcation in the circuit is analysed using the hopf bifurcation theory and the central manifold theorem in this paper. bifurcation points and bifurcation directions are derived in detail, which prove to be consistent with the previous bifurcation diagram. Numerical simulations and experimental results are given to verify the theoretical analysis. hopf bifurcation analysis can explain and predict the periodical orbit （oscillation） in Chen circuit with direct time delay feedback. bifurcation boundaries are derived using the hopf bifurcation analysis, which will be helpful for determining the parameters in the stabilisation of the originally chaotic circuit.

关键词： direct time delay feedback bifurcation diagram hopf bifurcation bifurcation boundary

hopf bifurcation and uncontrolled stochastic trafficinduced chaos in an RED-AQM congestion control system

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Chinese Physics B 2011年第9期20卷 92-97页

作者：王俊松袁睿翕高志伟王德进 School of Biomedical Engineering Tianjin Medical University School of Information Science Tsinghua University Department of Automation Tianjin University Department of Automation Tianjin University of Science and Technology

We study the hopf bifurcation and the chaos phenomena in a random early detection-based active queue man- agement （RED-AQM） congestion control system with a communication delay. We prove that there is a critical value of the communication delay for the stability of the RED-AQM control system. Furthermore, we show that the system will lose its stability and hopf bifurcations will occur when the delay exceeds the critical value. When the delay is close to its critical value, we demonstrate that typical chaos patterns may be induced by the uncontrolled stochastic traffic in the RED-AQM control system even if the system is still stable, which reveals a new route to the chaos besides the bifurcation in the network congestion control system. Numerical simulations are given to illustrate the theoretical results.

关键词： stability hopf bifurcation chaos stochastic tramc

hopf bifurcation analysis and circuit implementation for a novel four-wing hyper-chaotic system

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Chinese Physics B 2013年第8期22卷 325-332页

作者：薛薇齐国元沐晶晶贾红艳郭彦岭 Department of Automation Tianjin University of Science & Technology F'SATI/Department of Electrical Engineering Tshwane University of Technology

In the paper, a novel four-wing hyper-chaotic system is proposed and analyzed. A rare dynamic phenomenon is found that this new system with one equilibrium generates a four-wing-hyper-chaotic attractor as parameter varies. The system has rich and complex dynamical behaviors, and it is investigated in terms of Lyapunov exponents, bifurcation diagrams, Poincare maps, frequency spectrum, and numerical simulations. In addition, the theoretical analysis shows that the system undergoes a hopf bifurcation as one parameter varies, which is illustrated by the numerical simulation. Finally, an analog circuit is designed to implement this hyper-chaotic system.

关键词： hyper-chaos four-wing chaotic system one equilibrium hopf bifurcation circuit implementation

hopf bifurcation AND CHAOS OF FINANCIAL SYSTEM ON CONDITION OF SPECIFIC COMBINATION OF PARAMETERS

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Journal of Systems Science & Complexity 2008年第2期21卷 250-259页

作者： Junhai MA Yaqiang CUI Lixia LIU Management School of Tianjin University Tianjin 300072 China Tianjin University of Finance and Economics Tianjin 300222 China

This paper studies the global bifurcation and hopf bifurcation of one kind of complicated financial system with different parameter combinations. Conditions on which bifurcation happens, and the critical system structure when the system transforms from one kind of topological structure to another are studied as well. The criterion for identifying hopf bifurcation under different parameter combinations is also given. The chaotic character of this system under quasi-periodic force is finally studied. The bifurcation structure graphs are given when two parameters of the combination are fixed while the other parameter varies. The presence and stability of 2 and 3 dimensional torus bifurcation are studied. All of the Lyapunov exponents of the system with different bifurcation parameters and routes leading the system to chaos with different parameter combinations are studied. It is of important theoretical and practical meaning to probe the intrinsic mechanism of such continuous complicated financial system and to find the macro control policies for such kind of system.

关键词： Chaos complicated financial system equilibrium "drift" hopf bifurcation strange non- chaotic attractor.

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hopf bifurcation of a tumor immune model with time delay

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Frontiers of Mathematics in China 2022年第2期17卷 315-335页

作者： Yanhong YANG Shengmao FU College of Mathematics and Statistics Northwest Normal UniversityLanzhou 730070China

In this paper,a tumor immune model with time delay is ***,the stability of nonnegative equilibria is *** the time delay τ is selected as a bifurcation parameter and the existence of hopf bifurcation is ***,by using the canonical method and the central manifold theory,the criteria for judging the direction and stability of hopf bifurcation are given.

关键词： Tumor immune model time delay hopf bifurcation existence direction stability

hopf bifurcation and chaos in an inertial neuron system with coupled delay

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Science China(Technological Sciences) 2013年第9期56卷 2299-2309页

作者： GE JuHong XU Jian Department of Mathematics and Information Science He'nan University of Economics and Law School of Aerospace Engineering and Applied Mechanics Tongji University

In this paper, inertia is added to a simplified neuron system with time delay. The stability of the trivial equilibrium of the net- work is analyzed and the condition for the existence of hopf bifurcation is obtained by discussing the associated characteristic equation. hopf bifurcation is investigated by using the perturbation scheme without the norm form theory and the center man- ifold theorem. Numerical simulations are performed to validate the theoretical results and chaotic behaviors are observed. Phase plots, time history plots, power spectra, and Poincar6 section are presented to confirm the chaoticity. To the best of our knowledge, the chaotic behavior in this paper is new to the previously published works.

关键词： time delay inertia hopf bifurcation chaos

hopf bifurcation in general Brusselator system with diffusion

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Applied Mathematics and Mechanics(English Edition) 2011年第9期32卷 1177-1186页

作者：郭改慧吴建华任小红 College of Science Shaanxi University of Science and Technology College of Mathematics and Information Science Shaanxi Normal University

The general Brusselator system is considered under homogeneous Neumann boundary *** existence results of the hopf bifurcation to the ordinary differential equation （ODE） and partial differential equation （PDE） models are *** the center manifold theory and the normal form method,the bifurcation direction and stability of periodic solutions are ***,some numerical simulations are shown to support the analytical *** the same time,the positive steady-state solutions and spatially inhomogeneous periodic solutions are graphically shown to supplement the analytical results.

关键词： general Brusselator system hopf bifurcation diffusion stability