三元离散神经网络模型的稳定性与分岔分析
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摘要
本文针对三元离散神经网络模型的稳定性与分岔进行讨论。研究的课题主要有：平衡点的稳定性、周期解的存在性以及分岔方向等问题。对于模型的研究主要分为两个方面：一方面是不具时滞的三元离散神经网络模型；另一方面是具时滞的三元离散神经网络模型。在模型分析中,离散动力系统Hopf分岔理论和扩展的Jury判据理论在本文得到了广泛的应用。全文主要工作如下：
第一部分主要针对三个神经元十种连接方式做出分析和说明。并简单地给出相应神经网络模型线性化后得到的特征方程。
第二部分研究的是三元单向全连接(带自反馈)离散神经网络模型平衡点(0,0,0)的稳定性、出现Neimarik-Sacker分岔的条件及分岔方向等问题。
第三部分主要研究了具时滞的三元全连接(带自反馈)离散神经网络模型(时滞为k)平衡点(0,0,0)的渐近稳定性、D3-等变和多重周期解分析等问题。
第四部分主要对具时滞的三元非全连接(带自反馈)的离散神经网络模型(时滞为k)进行讨论,研究其平衡点(0,0,0)的稳定性及离散Hopf分岔的存在性。研究方法同第三部分,并得到了相关结论。
本文对上述研究成果在理论上进行了严格的证明,且在本文的第四章、第五章以及第六章所提到的三元离散神经网络模型在每章的第三部分进行了大量的数值模拟仿真实验。所得到的实验结果不仅对神经网络有很高的理论指导意义,而且具有较好的参考价值。
In this paper, an in-depth research on the stability and bifurcation of a three-dimension discrete neural network model is made in this thesis. On the one hand, a three-dimension discrete neural network model without delay is considered. On the other hand, a three-dimension discrete neural network model with delay is considered. Bifurcation theory on Discrete Dynamic System and Extensional Jury Criterion are extensively applied in this thesis. The main tasks are as follows.
In the first part, ten kinds of connection in the three neurons are considered. And we also give the corresponding characteristic equation of linearization discrete neural network model.
In the second part, we investigate the stability and bifurcation of a three-dimension with single-directional fully connected discrete neural network model without delay (with self-feedback) We discuss the asymptotically stability on equilibrium, the existence of Neimark-Sacker bifurcation and the bifurcation direction.
In the third part, we discuss the stability and bifurcation of a three-dimension with fully connected discrete neural network model with delay (with self-feedback) k is the time-delay. We discuss the asymptotically stability on equilibrium, D_3-equivariant and the existence of multiple periodic solutions and the bifurcation direction.
In the fourth part, we investigate the stability and bifurcation of a three-dimension with non-fully connected discrete neural network model with delay (with self-feedback) k is the time-delay. It is also using the same method with the third part and obtains some relevant results.
This paper makes strict theory proof and gives concrete computer simulation experiments. Not only do our experimental results illustrate the stability and bifurcation of a three-dimension discrete neural network model without delay and with delay, but also can be easily implemented in actual systems. Finally, computer simulations are performed to support the theoretical predictions.
第一部分主要针对三个神经元十种连接方式做出分析和说明。并简单地给出相应神经网络模型线性化后得到的特征方程。
第二部分研究的是三元单向全连接(带自反馈)离散神经网络模型平衡点(0,0,0)的稳定性、出现Neimarik-Sacker分岔的条件及分岔方向等问题。
第三部分主要研究了具时滞的三元全连接(带自反馈)离散神经网络模型(时滞为k)平衡点(0,0,0)的渐近稳定性、D3-等变和多重周期解分析等问题。
第四部分主要对具时滞的三元非全连接(带自反馈)的离散神经网络模型(时滞为k)进行讨论,研究其平衡点(0,0,0)的稳定性及离散Hopf分岔的存在性。研究方法同第三部分,并得到了相关结论。
本文对上述研究成果在理论上进行了严格的证明,且在本文的第四章、第五章以及第六章所提到的三元离散神经网络模型在每章的第三部分进行了大量的数值模拟仿真实验。所得到的实验结果不仅对神经网络有很高的理论指导意义,而且具有较好的参考价值。
In this paper, an in-depth research on the stability and bifurcation of a three-dimension discrete neural network model is made in this thesis. On the one hand, a three-dimension discrete neural network model without delay is considered. On the other hand, a three-dimension discrete neural network model with delay is considered. Bifurcation theory on Discrete Dynamic System and Extensional Jury Criterion are extensively applied in this thesis. The main tasks are as follows.
In the first part, ten kinds of connection in the three neurons are considered. And we also give the corresponding characteristic equation of linearization discrete neural network model.
In the second part, we investigate the stability and bifurcation of a three-dimension with single-directional fully connected discrete neural network model without delay (with self-feedback) We discuss the asymptotically stability on equilibrium, the existence of Neimark-Sacker bifurcation and the bifurcation direction.
In the third part, we discuss the stability and bifurcation of a three-dimension with fully connected discrete neural network model with delay (with self-feedback) k is the time-delay. We discuss the asymptotically stability on equilibrium, D_3-equivariant and the existence of multiple periodic solutions and the bifurcation direction.
In the fourth part, we investigate the stability and bifurcation of a three-dimension with non-fully connected discrete neural network model with delay (with self-feedback) k is the time-delay. It is also using the same method with the third part and obtains some relevant results.
This paper makes strict theory proof and gives concrete computer simulation experiments. Not only do our experimental results illustrate the stability and bifurcation of a three-dimension discrete neural network model without delay and with delay, but also can be easily implemented in actual systems. Finally, computer simulations are performed to support the theoretical predictions.
引文
[1]J. Hopfield. Neural Networks and Physical Systems with Emergent Collective Computational Abilities [J]. Proceedings of the National Academy of Sciences,1982, 79:2554～2558
[2]W. R. Zhao, W. Lin, R. S. Liu. Asymptotical Stability in Discrete-Time Neural Network [J]. IEEE Trans. Circuits Syst.Ⅰ,2002,49(10):1516～1520
[3]S. Mohamad, K. Gopalsamy. Dynamics of a Class of Discrete-Time Neural Networks and Their Continuous-Time Counterparts [J]. Math. Comput. Simulation,2000,53(1～2):1～39
[4]J. Ruan, J. P. Wang, D. D. Guo. Asymptotical Stability of Non-Antonomous Discrete-Time Neural Networks with Generalized Input-output Function [J]. Ann. of Diff. Equs,2004, 20(2):155～167
[5]吴然超,胡宗海,程玲华.多重时滞离散神经网络的指数稳定性[J].安徽大学学报(自然科学版),2008,32(4)：1～4
[6]J. Vance, S. Jagannathan. Discrete-Time Neural Network Output Feedback Control of Nonlinear Discrete-Time Systems in Non-Strict Form [J]. Automatica,2008, 44(4):1020～1027
[7]M. S. Peng, Y. Yuan. Complex Dynamics in Discrete Delayed Models with D4 Symmetry [J]. Chaos, Solitons and Fractals,2008,37(2):393～408
[8]B. M. Wang, J. G Jian. Stability and Hopf Bifurcation Analysis on a Four-Neuron BAM Neural Network with Distributed Delays [J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(2):189～204
[9]Z. Zhou, J. H. Wu. Stable Periodic Orbits in Nonlinear Discrete-Time Neural Networks with Delayed Feedback [J]. Computer and Mathematics with Applications,2003, 45(6～9):935～942
[10]周铁军,戴斌祥,刘一戎.一类二元离散神经网络周期解的存在性[J].湖南农业大学学报(自然科学版),2005,31(5)：565～569
[11]曹爱华,李雪梅.一类三元细胞神经网络的收敛性[J].吉首大学学报(自然科学版),2007,5
[12]陈燕芬.一类离散动力学系统的稳定性[J].高等数学研究,2006,9(4)：72～82
[13]于晋臣,张彩艳,彭明书.一类离散动力系统的混沌研究[J].昆明理工大学学报(理工版),2009,34(4)：101～104
[14]W. He, J. Gao. Stability and Bifurcation of a Class of Discrete-Time Neural Networks [J]. Math.Comput. Model,2007,31(10):2111～2122
[15]Q. T. Gan, R. Xu, W. H. Hu. Bifurcation Analysis for a Tri-neuron Discrete-Time BAM Neural Network with Delays [J]. Chaos, Solitons and Fractals,2009,42(4):2502～2511
[16]B. D. Zheng, Y. Zhang, C. R. Zhang. Stability and Bifurcation of a Discrete BAM Neural Network Model with Delays [J]. Chaos, Solitons and Fractals,2008,36(3):612～616
[17]朱伟,杨晓松.线性离散动力系统的稳定性判定准则[J].应用科学学报,2005,23(4)：432～434
[18]Q. K. Song, Z. D. Wang. Neural Networks with Discrete and Distributed Time-Varying Delays :A General Stability Analysis[J], Chaos, Solitons and Fractals,2008, 37(5):1538～1547
[19]W. Xiong, J. Gao. Global Exponential Stability of Discrete-Time Cohen-Grossberg Neural Networks [J]. Neurocomputing,2005,64:433～446
[20]D. J. Fan, J. J. Wei. Bifurcation Analysis of Discrete Survival Red Blood Cell Model [J]. Communications in Nonlinear Science and Numerical Simulation,2009,14(8):3358～3368
[21]H. Y. Zhao, L. Wang, C. X. Ma. Hopf Bifurcation and Stability Analysis on Discrete-Time Hopfield Neural Network with Delay [J]. Nonlinear Analysis:Real World Applications, 2008,9(1):103～113
[22]S. J. Guo, X.H. Tang, L. H. Huang. Bifurcation Analysis in a Discrete-Time Single-Directional Network with Delays [J]. Neurocomputing,2008,71(7～9):1422～1435
[23]杨慧,莫道宏,王良龙.一类离散神经网络模型的分支[J].合肥学院学报(自然科学版),2009,19(4)：16～19
[24]S. J. Guo, X. H. Tang, L. H. Huang. Stability and Bifurcation in Discrete System of Two Neurons with Delays [J]. Nonlinear Analysis:Real World Applications,2008, 9(4):1323～1335
[25]C. R. Zhang, B. D. Zheng. Stability and Bifurcation of a Two-Dimension Discrete Neural Network Model with Multi-Delays [J]. Chaos, Solitons and Fractals,2007,31(5): 1232～1242
[26]Z.Yuan, L. Huang, Y. Chen. Convergence and Periodicity of Solutions for a Discrete-Time Network Model of Two Neurons [J]. Math. Comp. Modeling,2002,35(9～10): 941～950
[27]周健君,周铁君,戴斌祥.一类二元离散神经网络周期解的存在性[J].岳阳职业技术学院学报,2004,19(4)：111～113
[28]Z. H. Yuan, D. W. Hu, L. H. Huang. Stability and Bifurcation Analysis on a Discrete Time Neural Network [J]. Journal of Computational and Applied Mathematics,2005,117(1): 89～100
[29]侯爱玉,姜小伟.一类二维离散动力系统的稳定性与分岔[J].数学理论与应用,2008,28(3)：84～88
[30]X. B. Zhou, Y. Wu, Y. Li, X. Yao. Stability and Hopf Bifurcation Analysis on a Two- Neuron Network with Discrete and Distributed Delays [J]. Chaos, Solitons and Fractals, 2009,40(3):1493～1505
[31]H. Y. Zhu, L. H. Huang. Asymptotic Behavior of a Discrete-time Network Model of Two Neurons [J]. Journal of Mathematical Research and Exposition,2004,24(2):267～272
[32]S. Guo, L. Huang. Periodic Oscillation for Discrete-Time Hopfield Neural Networks. Phys. Lett. A,2004,329(3):199～206
[33]E.Kaslik, St. Balint. Bifurcation Analysis for a Two-Dimensional Delayed Discrete-Time Hopfield Neural Network [J]. Chaos, Solitons and Fractals,2007,34(4):1245～1253
[34]Maria da Conceicao A Leite, Martin Golubitsky. Homogeneous Three-Cell Networks [J]. Nonlinearity,2006,19:2313～2363
[35]L. Li, Y. Yuan, Dynamics in Three Cells with Multiple Time Delays [J]. Nonlinear Analysis:Real World Applications,2008,9(3):725～746
[36]王军平.几类离散神经网络模型的动力学分析[D].复旦大学博士论文.2006
[37]宾红华.几类离散神经网络模型解得渐进性与周期性[D].湖南大学硕士论文.2002
[38]邹琳.离散神经网络的周期解及稳定性[D].湖南大学硕士论文.2004
[39]袁少良.带自反馈环状时滞细胞神经网络的分支与稳定性分析[D].湖南师范大学硕士论文.2009
[40]B. D. Zheng, L. J. Liang, C. R. Zhang. Extended Jury Criterion [J]. Science in China Series A:Mathematics,2009,39(10):1239～1260
[41]J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields [M]. New York:Springer-Verlag,1983
[42]S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos [M]. New York:Springer-Verlag,1990
[43]C. Robinson. Dynamical systems, stability, symbolic dynamical system and chaos (2nd ed) [M].London, New York, Washington(DC):Boca Raton,1999
[44]J. Carr. Applications of Center Manifold Theory [M]. New York:Springer-Verlag,1981
[45]Bernold Fiedler. Global Bifurcation of Periodic Solutions with Symmetry [M]. Berlin: Spinger-Verlag,1998
[46]B. D. Hassard, N. D. Kazarinoff, Y. H. Wan. Theory and Applications of Hopf Bifurcation [M]. Cambridge:Cambridge University Press,1981
[47]R. Seydel, Practical Bifurcation and Stability Analysis:From Equilibrium to Chaos [M].Berlin:Springer-Verlag,1994
[48]罗定,张祥,董梅芳.动力系统的定性与分支理论[M].北京：科学出版社,2001
[49]张锦炎,冯贝叶.常微分方程几何理论与分支问题[M].北京：北京大学出版社,2000
[50]C. R. Zhang, M. Z. Liu, B. D. Zheng. Hopf Bifurcation in Numerical Approximation of a Class Delay Differential Equations [J]. Appl. Math. Comput,2003,146(2～3):335～349
[51]M. S. Peng, Ahmet Ucar. The Use of Euler Method in Identification of Multiple Bifurcations and Chaotic Behavior in Numerical Approximation of Delay-differential Equations[J].Chaos, Solitons and Fractals,2004,21(4):883～891
[52]Z. H. Yuan, D. W. Hu, L. H. Huang. Stability and Bifurcation Analysis on a Discrete-Time System of Two Neurons [J]. Appl. Math. Lett.,2004,17(11):1239～1245
[53]M. S. Peng. Symmetry Breaking, Bifurcation, Periodicity and Chaos in the Euler Method for a Class of Delay Differential Equations [J]. Chaos, Solitons and Fractals,2005,24(5): 1287～1297
[54]A. K. Yuri. Elements of Applied Bifurcation Theory [M]. New-York:Springer-Verlag, 1995
[55]M. Golubitsky, I. N. Stewart, D. G. Schaeffer. Singularities and Groups in Bifurcation Theory [M]. New York:Springer-Verlag,1988
[2]W. R. Zhao, W. Lin, R. S. Liu. Asymptotical Stability in Discrete-Time Neural Network [J]. IEEE Trans. Circuits Syst.Ⅰ,2002,49(10):1516～1520
[3]S. Mohamad, K. Gopalsamy. Dynamics of a Class of Discrete-Time Neural Networks and Their Continuous-Time Counterparts [J]. Math. Comput. Simulation,2000,53(1～2):1～39
[4]J. Ruan, J. P. Wang, D. D. Guo. Asymptotical Stability of Non-Antonomous Discrete-Time Neural Networks with Generalized Input-output Function [J]. Ann. of Diff. Equs,2004, 20(2):155～167
[5]吴然超,胡宗海,程玲华.多重时滞离散神经网络的指数稳定性[J].安徽大学学报(自然科学版),2008,32(4)：1～4
[6]J. Vance, S. Jagannathan. Discrete-Time Neural Network Output Feedback Control of Nonlinear Discrete-Time Systems in Non-Strict Form [J]. Automatica,2008, 44(4):1020～1027
[7]M. S. Peng, Y. Yuan. Complex Dynamics in Discrete Delayed Models with D4 Symmetry [J]. Chaos, Solitons and Fractals,2008,37(2):393～408
[8]B. M. Wang, J. G Jian. Stability and Hopf Bifurcation Analysis on a Four-Neuron BAM Neural Network with Distributed Delays [J]. Communications in Nonlinear Science and Numerical Simulation,2010,15(2):189～204
[9]Z. Zhou, J. H. Wu. Stable Periodic Orbits in Nonlinear Discrete-Time Neural Networks with Delayed Feedback [J]. Computer and Mathematics with Applications,2003, 45(6～9):935～942
[10]周铁军,戴斌祥,刘一戎.一类二元离散神经网络周期解的存在性[J].湖南农业大学学报(自然科学版),2005,31(5)：565～569
[11]曹爱华,李雪梅.一类三元细胞神经网络的收敛性[J].吉首大学学报(自然科学版),2007,5
[12]陈燕芬.一类离散动力学系统的稳定性[J].高等数学研究,2006,9(4)：72～82
[13]于晋臣,张彩艳,彭明书.一类离散动力系统的混沌研究[J].昆明理工大学学报(理工版),2009,34(4)：101～104
[14]W. He, J. Gao. Stability and Bifurcation of a Class of Discrete-Time Neural Networks [J]. Math.Comput. Model,2007,31(10):2111～2122
[15]Q. T. Gan, R. Xu, W. H. Hu. Bifurcation Analysis for a Tri-neuron Discrete-Time BAM Neural Network with Delays [J]. Chaos, Solitons and Fractals,2009,42(4):2502～2511
[16]B. D. Zheng, Y. Zhang, C. R. Zhang. Stability and Bifurcation of a Discrete BAM Neural Network Model with Delays [J]. Chaos, Solitons and Fractals,2008,36(3):612～616
[17]朱伟,杨晓松.线性离散动力系统的稳定性判定准则[J].应用科学学报,2005,23(4)：432～434
[18]Q. K. Song, Z. D. Wang. Neural Networks with Discrete and Distributed Time-Varying Delays :A General Stability Analysis[J], Chaos, Solitons and Fractals,2008, 37(5):1538～1547
[19]W. Xiong, J. Gao. Global Exponential Stability of Discrete-Time Cohen-Grossberg Neural Networks [J]. Neurocomputing,2005,64:433～446
[20]D. J. Fan, J. J. Wei. Bifurcation Analysis of Discrete Survival Red Blood Cell Model [J]. Communications in Nonlinear Science and Numerical Simulation,2009,14(8):3358～3368
[21]H. Y. Zhao, L. Wang, C. X. Ma. Hopf Bifurcation and Stability Analysis on Discrete-Time Hopfield Neural Network with Delay [J]. Nonlinear Analysis:Real World Applications, 2008,9(1):103～113
[22]S. J. Guo, X.H. Tang, L. H. Huang. Bifurcation Analysis in a Discrete-Time Single-Directional Network with Delays [J]. Neurocomputing,2008,71(7～9):1422～1435
[23]杨慧,莫道宏,王良龙.一类离散神经网络模型的分支[J].合肥学院学报(自然科学版),2009,19(4)：16～19
[24]S. J. Guo, X. H. Tang, L. H. Huang. Stability and Bifurcation in Discrete System of Two Neurons with Delays [J]. Nonlinear Analysis:Real World Applications,2008, 9(4):1323～1335
[25]C. R. Zhang, B. D. Zheng. Stability and Bifurcation of a Two-Dimension Discrete Neural Network Model with Multi-Delays [J]. Chaos, Solitons and Fractals,2007,31(5): 1232～1242
[26]Z.Yuan, L. Huang, Y. Chen. Convergence and Periodicity of Solutions for a Discrete-Time Network Model of Two Neurons [J]. Math. Comp. Modeling,2002,35(9～10): 941～950
[27]周健君,周铁君,戴斌祥.一类二元离散神经网络周期解的存在性[J].岳阳职业技术学院学报,2004,19(4)：111～113
[28]Z. H. Yuan, D. W. Hu, L. H. Huang. Stability and Bifurcation Analysis on a Discrete Time Neural Network [J]. Journal of Computational and Applied Mathematics,2005,117(1): 89～100
[29]侯爱玉,姜小伟.一类二维离散动力系统的稳定性与分岔[J].数学理论与应用,2008,28(3)：84～88
[30]X. B. Zhou, Y. Wu, Y. Li, X. Yao. Stability and Hopf Bifurcation Analysis on a Two- Neuron Network with Discrete and Distributed Delays [J]. Chaos, Solitons and Fractals, 2009,40(3):1493～1505
[31]H. Y. Zhu, L. H. Huang. Asymptotic Behavior of a Discrete-time Network Model of Two Neurons [J]. Journal of Mathematical Research and Exposition,2004,24(2):267～272
[32]S. Guo, L. Huang. Periodic Oscillation for Discrete-Time Hopfield Neural Networks. Phys. Lett. A,2004,329(3):199～206
[33]E.Kaslik, St. Balint. Bifurcation Analysis for a Two-Dimensional Delayed Discrete-Time Hopfield Neural Network [J]. Chaos, Solitons and Fractals,2007,34(4):1245～1253
[34]Maria da Conceicao A Leite, Martin Golubitsky. Homogeneous Three-Cell Networks [J]. Nonlinearity,2006,19:2313～2363
[35]L. Li, Y. Yuan, Dynamics in Three Cells with Multiple Time Delays [J]. Nonlinear Analysis:Real World Applications,2008,9(3):725～746
[36]王军平.几类离散神经网络模型的动力学分析[D].复旦大学博士论文.2006
[37]宾红华.几类离散神经网络模型解得渐进性与周期性[D].湖南大学硕士论文.2002
[38]邹琳.离散神经网络的周期解及稳定性[D].湖南大学硕士论文.2004
[39]袁少良.带自反馈环状时滞细胞神经网络的分支与稳定性分析[D].湖南师范大学硕士论文.2009
[40]B. D. Zheng, L. J. Liang, C. R. Zhang. Extended Jury Criterion [J]. Science in China Series A:Mathematics,2009,39(10):1239～1260
[41]J. Guckenheimer, P. Holmes. Nonlinear Oscillations, Dynamical Systems and Bifurcations of Vector Fields [M]. New York:Springer-Verlag,1983
[42]S. Wiggins. Introduction to Applied Nonlinear Dynamical Systems and Chaos [M]. New York:Springer-Verlag,1990
[43]C. Robinson. Dynamical systems, stability, symbolic dynamical system and chaos (2nd ed) [M].London, New York, Washington(DC):Boca Raton,1999
[44]J. Carr. Applications of Center Manifold Theory [M]. New York:Springer-Verlag,1981
[45]Bernold Fiedler. Global Bifurcation of Periodic Solutions with Symmetry [M]. Berlin: Spinger-Verlag,1998
[46]B. D. Hassard, N. D. Kazarinoff, Y. H. Wan. Theory and Applications of Hopf Bifurcation [M]. Cambridge:Cambridge University Press,1981
[47]R. Seydel, Practical Bifurcation and Stability Analysis:From Equilibrium to Chaos [M].Berlin:Springer-Verlag,1994
[48]罗定,张祥,董梅芳.动力系统的定性与分支理论[M].北京：科学出版社,2001
[49]张锦炎,冯贝叶.常微分方程几何理论与分支问题[M].北京：北京大学出版社,2000
[50]C. R. Zhang, M. Z. Liu, B. D. Zheng. Hopf Bifurcation in Numerical Approximation of a Class Delay Differential Equations [J]. Appl. Math. Comput,2003,146(2～3):335～349
[51]M. S. Peng, Ahmet Ucar. The Use of Euler Method in Identification of Multiple Bifurcations and Chaotic Behavior in Numerical Approximation of Delay-differential Equations[J].Chaos, Solitons and Fractals,2004,21(4):883～891
[52]Z. H. Yuan, D. W. Hu, L. H. Huang. Stability and Bifurcation Analysis on a Discrete-Time System of Two Neurons [J]. Appl. Math. Lett.,2004,17(11):1239～1245
[53]M. S. Peng. Symmetry Breaking, Bifurcation, Periodicity and Chaos in the Euler Method for a Class of Delay Differential Equations [J]. Chaos, Solitons and Fractals,2005,24(5): 1287～1297
[54]A. K. Yuri. Elements of Applied Bifurcation Theory [M]. New-York:Springer-Verlag, 1995
[55]M. Golubitsky, I. N. Stewart, D. G. Schaeffer. Singularities and Groups in Bifurcation Theory [M]. New York:Springer-Verlag,1988
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