2006年, 第19卷, 第1期　刊出日期：2006-03-20

  

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  STUDYING COMPLEX ADAPTIVE SYSTEMS

  John H. Holland

  Journal of Systems Science and Complexity. 2006, 19(1): 1-008.

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  Complex adaptive systems (cas) -- systems that involve many components that adapt or learn as they interact -- are at the heart of important contemporary problems. The study of cas poses unique challenges: Some of our most powerful mathematical tools, particularly methods involving fixed points, attractors, and the like, are of limited help in understanding the development of cas. This paper suggests ways to modify research methods and tools, with an emphasis on the role of computer-based models, to increase our understanding of cas.
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  OPTIMAL STARTING PRICE FOR EBAY-LIKE ONLINE AUCTIONS

  Hai YU;Shouyang WANG;Chuangyin DANG

  Journal of Systems Science and Complexity. 2006, 19(1): 9-021.

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  Reserve price auctions are one of hot research issues in traditional auction theory. Here we study the starting price in an online auction, the counterpart of the public reserve price in a traditional auction. By considering three features of eBay-like online auctions: stochastic entry of bidders (subject to Poisson process), insertion fee proportional to the starting price, and time discount, we have analyzed the properties of extremum points of the starting price for maximizing the seller's expected revenue, and found that, under certain conditions, the optimal starting price should be at the lowest allowable level, which is contrary to the results from the classic auction theory and finds its optimality in reality. We have also developed a general extended model of multistage auctions and carried out analysis on its properties. At last, some directions for further research are also put forward.
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  IDENTIFICATION ERROR BOUNDS AND ASYMPTOTIC DISTRIBUTIONS FOR SYSTEMS WITH STRUCTURAL UNCERTAINTIES

  Gang George YIN;Shaobai KAN;Le Yi WANG

  Journal of Systems Science and Complexity. 2006, 19(1): 22-035.

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  This work is concerned with identification of systems that are subject to not only measurement noises, but also structural uncertainties such as unmodeled dynamics, sensor nonlinear mismatch, and observation bias. Identification errors are analyzed for their dependence on these structural uncertainties. Asymptotic distributions of scaled sequences of estimation errors are derived.
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  ANALYSIS AND COMPUTATIONAL ALGORITHM FOR QUEUES WITH STATE-DEPENDENT VACATIONS I: G/M(n)/1/K

  Xiuli CHAO;Ayyar Rahman

  Journal of Systems Science and Complexity. 2006, 19(1): 36-053.

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  In this paper we study a queueing system with state-dependent services and state-dependent vacations, or simply $G/M(n)/1/K$. Since the service rate is state-dependent, this system includes $G/M/c$ and $G/M/c/K$ queues with various types of station vacations as special cases. We provide a recursive algorithm using the supplementary variable technique to numerically compute the stationary queue length distribution of the system. The only input requirement is the Laplace-Stieltjes transform of the interarrival distribution as well as the state-dependent service rate and state-dependent vacation rate. In a subsequent companion paper, we study its dual system $M(n)/G/1/K$ queue with state-dependent vacations.
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  SOFT CONTROL ON COLLECTIVE BEHAVIOR OF A GROUP OF AUTONOMOUS AGENTS BY A SHILL AGENT

  Jing HAN;Ming LI;Lei GUO

  Journal of Systems Science and Complexity. 2006, 19(1): 54-062.

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  This paper asks a new question: how can we control the collective behavior of self-organized multi-agent systems? We try to answer the question by proposing a new notion called `soft Control', which keeps the local rule of the existing agents in the system. We show the feasibility of soft control by a case study. Consider the simple but typical distributed multi-agent model proposed by Vicsek et al. for flocking of birds: each agent moves with the same speed but with different headings which are updated using a local rule based on the average of its own heading and the headings of its neighbors. Most studies of this model are about the self-organized collective behavior, such as synchronization of headings. We want to intervene in the collective behavior (headings) of the group by soft control. A specified method is to add a special agent, called a `Shill', which can be controlled by us but is treated as an ordinary agent by other agents. We construct a control law for the shill so that it can synchronize the whole group to an objective heading. This control law is proved to be effective analytically and numerically. Note that soft control is different from the approach of distributed control. It is a natural way to intervene in the distributed systems. It may bring out many interesting issues and challenges on the control of complex systems.
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  AGGREGATION OF FUZZY OPINIONS UNDER GROUP DECISION-MAKING BASED ON SIMILARITY AND DISTANCE

  Chengguo LU;Jibin LAN;Zhongxing WANG

  Journal of Systems Science and Complexity. 2006, 19(1): 63-071.

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  In this article, a new method for aggregating fuzzy individual opinions into a group consensus opinion is proposed. To obtain the aggregation weights of each individual opinion, a consistency index of each expert with the other experts is introduced based on similarity and distance. The importance of each expert is also taken into consideration in the process of aggregation. Finally, a numerical example is presented to illustrate the efficiency of the procedure.
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  THE EXISTENCE OF ORBITS CONNECTING CRITICAL POINTS OF DIFFERENTIAL EQUATIONS DEPENDING ON A PARAMETER

  Shuxiang YU

  Journal of Systems Science and Complexity. 2006, 19(1): 72-075.

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  Using the concept of an isolated invariant set, some existence criteria of orbits connecting two critical points bifurcating from a single critical point for ordinary differential equations depending on a parameter are given.
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  A DYNAMIC APPROACH TO CALCULATE SHADOW PRICES OF WATER RESOURCES FOR NINE MAJOR RIVERS IN CHINA

  Jing HE;Xikang CHEN;Yong SHI

  Journal of Systems Science and Complexity. 2006, 19(1): 76-087.

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  China is experiencing from serious water issues. There are many differences among the Nine Major Rivers basins of China in the construction of dikes, reservoirs, floodgates, flood discharge projects, flood diversion projects, water ecological construction, water conservancy management, etc. The shadow prices of water resources for Nine Major Rivers can provide suggestions to the Chinese government. This article develops a dynamic shadow prices approach based on a multiperiod input--output optimizing model. Unlike previous approaches, the new model is based on the dynamic computable general equilibrium (DCGE) model to solve the problem of marginal long-term prices of water resources. First, definitions and algorithms of DCGE are elaborated. Second, the results of shadow prices of water resources for Nine Major Rivers in 1949--2050 in China using the National Water Conservancy input--holding--output table for Nine Major Rivers in 1999 are listed. A conclusion of this article is that the shadow prices of water resources for Nine Major Rivers are largely based on the extent of scarcity. Selling prices of water resources should be revised via the usage of parameters representing shadow prices.
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  THE RANK AND COEXPONENT OF A FINITE P-GROUP

  Yujie MA

  Journal of Systems Science and Complexity. 2006, 19(1): 88-092.

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  In this paper, we present a sharp bound for the rank of a finite $p$-group in terms of its coexponent. As to finite $p$-groups with $p$ odd, we also give a sufficient condition for which the normal rank is equal to its rank.
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  $D$-$B$-PREINVEX TYPE MAPPINGS

  Jianwen PENG;Xinmin YANG;Weidong RONG

  Journal of Systems Science and Complexity. 2006, 19(1): 93-100.

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  In this paper, such new definitions as $D$-$B$-preinvexity, strictly $D$-$B$-preinvexity and explicitly $D$-$B$-preinvexity for vector-valued mappings are firstly introduced. Then, a sufficient condition of $D$-$B$-preinvex mappings is shown. And then the relationship between the explicitly $D$-$B$-preinvexity and the strictly $D$-$B$-preinvexity is discussed. Finally, some properties of $D$-$B$-preinvex type mappings are given.
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  SEMI ON-LINE SCHEDULING PROBLEM FOR MAXIMIZING THE MINIMUM MACHINE COMPLETION TIME ON TWO UNIFORM MACHINES

  Runzi LUO;Shijie SUN;Wenping HUANG

  Journal of Systems Science and Complexity. 2006, 19(1): 101-107.

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  In this paper, we consider a semi on-line version on two uniform machines $M_i$, $i=1,2$, where the processing time of the largest job is known in advance. A speed $s_i(s_1=1$, $1\leq s_2=s)$ is associated with machine $M_i$. Our goal is to maximize the $C_{\min}$. We give a $C_{\min2}$ algorithm and prove its competitive ratio is at most $\frac{2s+1}{s+1}$. We also claim the $C_{\min2}$ algorithm is tight and the gap between the competitive ratio of $C_{\min2}$ algorithm and the optimal value is not greater than $0.555$. It is obvious that our result coincides with that given by He for $s=1$.
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  A NOTE ON THE RIGHT SPREAD ORDER ASSOCIATED WITH EXPONENTIAL DISTRIBUTIONS

  Xiaohu LI

  Journal of Systems Science and Complexity. 2006, 19(1): 108-113.

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  It is shown that the total life of a parallel system with independent and identical (i.i.d.) exponential components is smaller in the right spread order than an exponential life with the same mean as the system. As applications, simple upper bounds for the mean and the variance of the life length of a parallel system with i.i.d. NBUE components are established, as well as the preservation property of the convolution of NBUE and exponential random variables.
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  EXISTENCE AND UNIQUENESS OF ENDEMIC STATES FOR THE AGE-STRUCTURED SEIR EPIDEMIC MODEL

  Xuezhi LI;Jing CHEN

  Journal of Systems Science and Complexity. 2006, 19(1): 114-127.

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  An age-structured SEIR epidemic model of a vertically as well as horizontally transmitted disease is investigated. Threshold results for the existence of endemic states are established for most cases. Under certain conditions, uniqueness is also shown. Threshold used are explicitly computable in term of demographic and epidemiological parameters of the model.
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  THE RELATIONSHIPS OF THREE ELEMENTARY CELLULAR AUTOMATA

  Zhisong JIANG

  Journal of Systems Science and Complexity. 2006, 19(1): 128-136.

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  Limit language complexity of cellular automata which is first posed by S. Wolfram has become a new branch of cellular automata. In this paper, we obtain two interesting relationships between elementary cellular automata of rules 126, 146(182) and 18, and prove that if the limit language of rule 18 is not regular, nor are the limit languages of rules 126 and 146(182).
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  ULTIMATE STABILITY OF A TYPE OF CHARACTERISTIC EQUATION WITH DELAY DEPENDENT PARAMETERS

  Jianquan LI;Zhien MA

  Journal of Systems Science and Complexity. 2006, 19(1): 137-144.

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  Delay differential systems are widely used in many different fields. It is important to determine the local stability of their equilibria. For systems with delay dependent parameters, the stability analysis of equilibria is complicated and difficult. In this paper, we shall investigate the ultimate stability of a type of characteristic equation with delay dependent parameters. Our results show that the characteristic equation with delay dependent parameters may be one of ultimately stable, ultimately unstable, and alternate between stable and unstable. Applying our results, the ultimate stability can be often decided directly and need not appeal to mathematic software. Two examples are given in this paper.