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Investigation of a Unified Chaotic System and Its Synchronization by Simulations

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Chinese Physics Letters 2010年第6期27卷 31-34页

作者： WU Qing-Chu FU Xin-Chu michael small Department of Mathematics Shanghai University Shanghai 200444 College of Mathematics and Information Science Jiangxi Normal University Nanchang 330022 Department of Electronic and Information Engineering Hong Kong Polytechnic University Hung Horn Kowloon Hong Kong

We investigate a unified chaotic system and its synchronization including feedback synchronization and adaptive synchronization by numerical simulations. We propose a new dynamical quantity denoted by K, which connects adaptive synchronization and feedback synchronization, to analyze synchronization schemes. We find that K can estimate the smallest coupling strength for a unified chaotic system whether it is complete feedback or one-sided feedback. Based on the previous work, we also give a new dynamical method to compute the leading Lyapunov exponent.

关键词： Synchronization Adaptation Adaptability

Dynamical behaviour of an epidemic on complex networks with population mobility

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Chinese Physics B 2009年第9期18卷 3639-3646页

作者：张海峰 small michael 傅新楚汪秉宏 Department of Modern Physics University of Science and Technology of China School of Mathematical Science Anhui University Department of Electronic and Information Engineering Hong Kong Polytechnic University Department of Mathematics Shanghai University

In this paper, we study the dynamical behaviour of an epidemic on complex networks with population mobility. In our model, the number of people on each node is unrestricted as the nodes of the network are considered as cities, communities, and so on. Because people can travel between different cities, we study the effect of a population＇s mobility on the epidemic spreading. In view of the population＇s mobility, we suppose that the susceptible individual can be infected by an infected individual in the same city or other connected cities. Simulations are presented to verify our analysis.

关键词： complex network mobility heterogeneity epidemic threshold

Random complex networks

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National Science Review 2014年第3期1卷 357-367页

作者： michael small Lvlin Hou Linjun Zhang School of Mathematics and Statistics The University of Western Australia College of Information Systems and Management National University of Defense Technology Department of Statistics and Finance University of Science and Technology of China

Exactly what is meant by a ‘complex’ network is not clear; however, what is clear is that it is something other than a random graph. Complex networks arise in a wide range of real social, technological and physical systems. In all cases, the most basic categorization of these graphs is their node degree *** groups of complex networks may exhibit additional interesting features, including the so-called small-world efect or being scale-free. here are many algorithms with which one may generate networks with particular degree distributions(perhaps the most famous of which is preferential atachment). In this paper, we address what it means to randomly choose a network from the class of networks with a particular degree distribution, and in doing so we show that the networks one gets from the preferential atachment process are actually highly pathological. Certain properties(including robustness and fragility) which have been atributed to the(scale-free) degree distribution are actually more intimately related to the preferential atachment growth mechanism. We focus here on scale-free networks with power-law degree sequences—but our methods and results are perfectly generic.

关键词： complex networks scale-free networks random graph Markov chain Monte Carlo power-law network robustness

A new piecewise linear Chen system of fractional-order:Numerical approximation of stable attractors

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Chinese Physics B 2015年第6期24卷 216-224页

作者： Marius-F.Danca M.A.Aziz-Alaoui michael small Department of Mathematics and Computer Science Emanuel University of Oradea Romanian Institute of Science and Technology Normandie University ULH LMAHF-76600 Le Havre FR CNRS 3335 ISCN25 rue Philippe Lebon 76600 Le HavreFrance School of Mathematics and Statistics University of Western Australia

In this paper we present a new version of Chen＇s system： a piecewise linear （PWL） Chert system of fractional-order. Via a sigmoid-like function, the discontinuous system is transformed into a continuous system. By numerical simulations, we reveal chaotic behaviors and also multistability, i.e., the existence of small pararheter windows where, for some fixed bifurcation parameter and depending on initial conditions, coexistence of stable attractors and chaotic attractors is possible. Moreover, we show that by using an algorithm to switch the bifurcation parameter, the stable attractors can be numerically approximated.

关键词： PWL Chen attractor of fractional-order parameter switching Cellina's Theorem Filippov regu-larization Sigmoid function bifurcation diagram

Network science meets algebraic topology

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National Science Review 2019年第6期6卷 1064-1065页

作者： Lingqing Shen David M.Walker michael small Department of Mathematics Nanjing University Department of Mathematics & Statistics University of Western Australia Mineral Resources Commonwealth Scientific and Industrial Research Organisation

Network science is largely consumed with the study of graphs with heterogeneous degree: typically large graphs with no strong topological symmetry. Network science borrows approaches from statistical physics to understand this heterogeneous structure, in a manner quite distinct from the rich symmetry of the graphs that are studied by algebraic graph theorists. Shi et al. [1] move toward

关键词： Network science meets algebraic topology

Different Epidemic Models on Complex Networks

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Communications in Theoretical Physics 2009年第7期52卷 180-184页

作者： ZHANG Hai-Feng michael small FU Xin-Chu Department of Modern Physics University of Science and Technology of China Hefei 230026 China School of Mathematical Science Anhui University Hefei 230039 China Department of Electronic and Information Engineering Hong Kong Polytechnic University Hung Hom Kowloon Hong Kong Department of Mathematics Shanghai University Shanghai 200444 China

Models for diseases spreading are not just limited to SIS or SIR. For instance, for the spreading of AIDS/HIV, the susceptible individuals can be classified into different cases according to their immunity, and similarly, the infected individuals can be sorted into different classes according to their infectivity. Moreover, some diseases may develop through several stages. Many authors have shown that the individuals＇ relation can be viewed as a complex network. So in this paper, in order to better explain the dynamical behavior of epidemics, we consider different epidemic models on complex networks, and obtain the epidemic threshold for each ease. Finally, we present numerical simulations for each case to verify our results.

关键词： epidemic threshold scale-free network diseases spreading multiple-staged infectivity rate

STAGED PROGRESSION MODEL FOR EPIDEMIC SPREAD ON HOMOGENEOUS AND HETEROGENEOUS NETWORKS

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Journal of Systems Science & Complexity 2011年第4期24卷 619-630页

作者： Haifeng ZHANG michael small Xinchu FU School of Mathematical Sciences Anhui University Hefei 230039 China. Department of Electronic and Information Engineering Hong Kong Polytechnic University Hung HornKowloon Hong Kong China. Department of Mathematics Shanghai University Shanghai 200444 China.

In this paper, epidemic spread with the staged progression model on homogeneous and heterogeneous networks is studied. First, the epidemic threshold of the simple staged progression model is given. Then the staged progression model with birth and death is also considered. The case where infectivity is a nonlinear function of the nodes＇ degree is discussed, too. Finally, the analytical results are verified by numerical simulations.

关键词： Complex network epidemic heterogenous homogeneous the staged progression model.

Leverage Effects of Rich-club on Transitivity and Assortativity of Complex Networks

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Leverage Effects of Rich-club on Transitivity and Assortativ...

Gambling with Chaos How to use nonlinear dynamics to beat the casino

第六届全国网络科学论坛暨第二届全国混沌应用研讨会

作者： michael small Department of Electronic Engineering The Hong Kong Polytechnic University

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Gambling with Chaos How to use nonlinear dynamics to beat th...