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研究生： 林正傑
Lin, Zheng-Jie
論文名稱： A Linear Dynamical System
一類線性動力系統
指導教授： 鄭穗生
Cheng, Sui-Sun
口試委員:
學位類別： 碩士
Master
系所名稱： 理學院 - 數學系
Department of Mathematics
論文出版年： 2009
畢業學年度： 97
語文別： 英文
論文頁數： 31
中文關鍵詞： Economic model 、Maxnet network
相關次數： 點閱：30  下載：0 
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    • A linear dynamical model of the form x^(t+1)=M_nx^(t), where M_n is an n by n matrix with diagonal elments alpha and off diagonal elements beta, is studied. We find that each solution may be a constant, 2-perioidc, convergent, asymptotic 2-periodic, divergent, or oscillatory sequence. Applications of our study include an economic model and the generalized Maxnet network for locating maximal values.

    1 Introduction..........................................1 2 Preliminary Results...................................5 3 Individual Asymptotic Behaviors.......................9 4 Cooperative Behaviors.................................12 5 Change of Sign of x_m^(t).............................17 5.1 (I) x^(0) = 0.......................................17 5.2 (II) x^(0) > 0......................................17 5.3 (III) x^(0) < 0.....................................21 6 Applications..........................................24 6.1 Economic Systems....................................24 6.2 Maxnet Systems......................................26 7 Remarks...............................................30 8 References............................................31

    [1] J. T. Sandefur, Discrete Dynamical Modeling, Oxford University Press, 1993.
    [2] J. P. F. Sum and P. K. S. Tam, Note on the Maxnet Dynamics, Neural Computation, 8(1996),
    491–499

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