石至文（Chih-Wen Shih）教授

聯絡方式

• Email: math.101@nycu.edu.tw
• 電話: 03-571-2121 ext. 56409
• 傳真: 03-572-4679
• 地址: 新竹市大學路1001號 陽明交通大學 應用數學系
• 相關網站:    

近兩學期教授課程

• 113 學年度第一學期：
  • 常微分方程(一)
  • 微積分甲(一)


• 112 學年度第二學期：
  • 微積分甲(二)

履歷

• 學歷
  • 紐約州立大學水牛城分校 數學研究所 博 士
  • 紐約州立大學水牛城分校 數學研究所 碩 士
  • 國立交通大學應用數學系 學 士
• 學術專長暨研究領域
  • 微分方程
  • 動態系統
  • 生物數學
• 學術經歷與榮譽
  • 國家理論科學中心中心科學家(2009-2015)
  • 國立交通大學應用數學系系主任 (2005/08 - 2007/07 )
  • 國立交通大學應用數學系教授 (2000/08 - )
  • 國立交通大學應用數學系副教授 (1990/08 - 2000/07)
  • Visiting Scientist, School of Mathematics and Center for Dynamical Systems and Nonlinear Studies, Georgia Institute of Technology (1997-1998)
  • Visiting Scientist, Department of Mathematics, UCLA (2002 Spring)
  • Visiting Scholar, Mathematical Biosciences Institute, Ohio State University (2007-2008)


• 近五年研究計劃
  • 神經場模型的數學研究　(109-2115-M-009-002-MY2)
  • 耦合系統之鎖相解　（107-2115-M-009-003-MY2）
  • 生物律動之數學模型及分析(101-2115-M-009-002-MY2)
  • 延遲性耦合震盪系統(98-2115-M-009-012-MY3)
  • 延遲型方程的穩定性與分歧性分析(95-2115-M-009-016-MY3)
  • 類神經網路的數學研究(3/3)(94-2115-M-009-001-)

研究趣向

• 近期的研究興趣主要在於一些生物現象的數學模型分析；包含細胞分化(cell differentiation)、骨節生成(somitogenesis)、基因調控(gene regulation)、神經系統(nerval system)、生態系統(ecological system)。探討將動態學理論應用於對這些數學模型方程式的了解。另有研究興趣為有關類神經網路 (neural networks) 之數學理論。各種類神經網路之數學模式一般可以描述為連續時間之動態系統（微分方程）或離散時間之動態系統。所以,可以說研究的內容是探討某種形式的動態系統解的行為與性質。其中，最基本的問題是探討系統中解的收歛性(convergence of dynamics)。亦即，在何種條件下，解一定會趨近於一平衡態。其次,同感興趣的是混沌動態行為的探測。由於類神經網路之模式多為高維度空間之動態系統，如何知道在各種神經元間之耦合係數與不同的threshold條件下，解行為的特性，是重要的研究課題。 
• 類神經網路在各種科學領域中已有很廣泛的應用。如圖形辨識(pattern recognition)，訊號處理(signal processing)，計算方法(computations)，組合最優化問題(combinatorial optimization problem)，電路理論(circuit theory)等。這許多的應用事實上是建立在幾個神經網路模式之基本理論上的。

著作選集

(A)   Refereed Papers：

• Chang-Yuan Cheng and Chih-Wen Shih*, 2005, “Pattern formations and spatial entropy for spatially discrete diffusion equations”, Physica D 204, 135-160. (SCI-Applied Math)
• Liang Zhao, Ying-Cheng Lai* and Chih-Wen Shih, 2005, “Transition to intermittent chaotic Synchronization”, Phys. Rev. E 72, 036212. (SCI-Math-Physics)
• Chang-Yuan Cheng, Kuang-Hui Lin and Chih-Wen Shih*, 2006, “Multistability in recurrent neural networks”, SIAM J. Applied Mathematics, Vol.66, 4 , 1301-1320 (SCI-Applied Math)  (NSC 94-2115-M-009-001-)
• Chang-Yuan Cheng, Kuang-Hui Lin and Chih-Wen Shih*, 2007, “Multistability and convergence in delayed neural networks”, Physica D 225, 61-47. (SCI-Applied Math) (NSC 94-2115-M-009-001-)
• Kuang-Hui Lin and Chih-Wen Shih*, 2007, “Multiple almost periodic solutions in nonautonomous delayed neural network”, Neural Computation, 19, 12, 3392-3420. (SCI -Artificial intelligence)  (NSC 95-2115-M-009-016-MY3)
• Shyan-Shiou Chen and Chih-Wen Shih*, 2007, “Transiently chaotic neural networks with piecewise linear output functions” Chaos, Solitons and Fractals, 39, 717-730. (SCI- Math.-Interdisciplinary applications)
• Chang-Yuan Cheng and Chih-Wen Shih*, 2008, “Complete stability in multistable delayed neural networks”, Neural Computation, 21, 719-740. (SCI-Artificial Intelligence) (NSC 95-2115-M-009-016-MY3)
• Chih-Wen Shih* and Jui-Pin Tseng, 2008,“Convergent dynamics for multistable delayed neural networks”, Nonlinearity 21, 2361-2389.(SCI-Applied Math) (NSC 95-2115-M-009-016-MY3)
• Chih-Wen Shih* and Jui-Pin Tseng, 2009, “Global consensus for discrete-time competitive systems”, Chaos, Solitons and Fractals, 41, 302-310. (SCI-Math-Interdisciplinary applications)
• Avner Friedman, Chiu-Yen Kao, and Chih-Wen Shih*, 2009, “Asymptotic phases in a cell differentiation model”, J. Differential Equations 247, 736-769. (SCI-Math).
• Chih-Wen Shih* and Jui-Pin Tseng, 2011, “Global synchronization and asymptotic phases for a ring of identical cells with delayed coupling”, SIAM J. Math. Anal., Vol. 43, 4, 1667-1697. (SCI-Applied Math) (NSC 98-2115-M-009-012-MY3)
• Kang-Ling Liao, Chih-Wen Shih*, 2011,“Snapback repellers and homoclinic orbits for multi-dimensional maps”, J. Math. Anal. Appl., 386, 387-400. (SCI-Applied Math)
• Avner Friedman, Chiu-Yen Kao, and Chih-Wen Shih*, 2012, “Asymptotic limit in a cell differentiation model with consideration of transcription”, J. Differential Equations 252, 5679-5711. (SCI-Math).
• Kang-Ling Liao, Chih-Wen Shih* and Jui-Pin Tseng, 2012, “Synchronized oscillations in a mathematical model of segmentation in zebrafish”, Nonlinearity 25, 869–904. (SCI-Applied Math) (NSC 98-2115-M-009-012-MY3)
• Kang-Ling Liao, Chih-Wen Shih*, 2012,“A lattice model on somitogenesis of zebrafish”, Discrete and Continuous Dynamical Systems –Series B, 17 (8), 2789-2814. (SCI-Applied Math) (NSC 98-2115-M-009-012-MY3)
• Chih-Wen Shih*, Jui-Pin Tseng, 2013, “A general approach to synchronization of coupled cells”, SIAM J. Applied Dynamical Systems, Vol.12, No. 3, 1354-1393.
• Kuang-Hui Lin, Yuan Lou, Chih-Wen Shih*, Tze-Hung Tsai, 2014, “Global dynamics for two-species competition in patchy environment”, Mathematical Biosciences and Engineering, Vol. 11, No. 4, 947-970.
• Chang-Yuan Cheng, Kuang-Hui Lin, Chih-Wen Shih, Jui-Pin Tseng, 2015,“Multistability for delayed neural networks via sequential contracting”, IEEE Transactions on Neural Networks and Learning Systems, VOL.26, NO.12, 3109-3122.
• Chiu-Yen Kao, Chih-Wen Shih, Chang-Hong Wu, 2016,“Absolute stability and synchronization in neural field models with transmission delays”, Physica D, 328-329, 21-33.
• Kuan-Wei Chen, Kang-Ling Liao,Chih-Wen Shih, 2018, The kinetics in mathematical models on segmentation clock genes in zebrafish, J. Mathematical Biology, 76(1-2), 97-150
• Kang-Ling Liao, Chih-Wen Shih, Chi-Jer Yu, 2018, The snapback repellers for chaos in multidimensional maps, J. Computational Dynamics, Vo. 5, No. 1, 81-92
• Chang-Yuan Cheng, Kuang-Hui Lin, Chih-Wen Shih, 2019, Coexistence and extinction for two competing species in patchy environments, Mathematical Biosciences and Engineering, Vol. 16, No. 2, 909-946.
• Chih-Wen Shih, Jui-Pin Tseng, 2020, From approximate synchronization to identical synchronization in coupled systems, DCDS-B, Vol. 25, No. 9, 3677-3714 
• Kuan-Wei Chen, Chih-Wen Shih, 2021,　Collective oscillations in coupled-cell systems, Bulletin of Mathematical Biology, 83:62, 1-60.
• Chang-Yuan Cheng*, Kuang-Hui Lin, Chih-Wen Shih, “Intra- and Inter-specific competitions of two stage-structured species in a patchy environment”, 2022, J. Dynamics and Differential Equations, https://doi.org/10.1007/s10884-022-10229-z
• Chih-Wen Shih*, Chia-Hsin Yang, “Hopf bifurcation analysis for models on genetic negative feedback loops”, 2022, J. Mathematical Analysis and Applications, 516, 126537
• Chih-Wen Shih*, Jui-Pin Tseng, Chang-Hong Wu, Absolute stability and synchronization in second-order neural fields with conduction delays, SIAM J. Applied Dynamical Systems, 22(2), 2023, 878-917

• Kuan-Wei Chen, Chih-Wen Shih*, Phase-locked solutions of a coupled pair of nonidentical oscillators, J. Nonlinear Science, 34(14), 2024 

(C)   Others：

1. Shyan-Shiou Chen and Chih-Wen Shih*, Solving TSP via Neural Networks, in Traveling Salesman Problem, Editor: Federico Greco, I-Tech Education and Publishing, 2008.
2. Kang-Ling Liao, Chih-Wen Shih* and Jui-Pin Tseng, Multidimensional Dynamics: From Simple to Complicated, In Discrete Time Systems, Editor: Mario Alberto Jordan, I-Tech Education and Publishing, April 2011

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