publications
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Research Interests:

Global asymptotic stability, periodic behavior, and bifurcation phenomena in functional differential equations.

 

Book:

Shangjiang Guo, Jianhong Wu, Bifurcation Theory of Functional Differential Equations. Applied Mathematical Science, Volume 184, Springer: New York, 2013.

 

Selected Publications:

Year 2000

[1] S.Guo, L.Huang,Oscillation and existence of positive solutions of difference equations with positive and negative coefficients, J. Hunan University, 2000, 27(6),1-3.

 

Year 2001

[2] S.Guo, L.Huang, Asymptotic behavior of a two-neuron network, J. Basic Science and Engineering, 2001, 9, 111-119.  

[3] S.Guo, L.Huang, A. Chen, Existence of positive solutions and oscillatory solutions of differential equations with positive and negative coefficientsMathematical Sciences Research Hot-Line, 2001, 5(6), 59-65.

 

Year 2002

[4] S.Guo, L.Huang, Oscillation and existence of positive solutions of differential equations with positive, negative coefficientsAnnals of Differential Equations2002, 18 (4): 344-351

 

Year 2003

[5] S.Guo, L.Huang, J. Wu, Global attractivity of a synchronized periodic orbit in a delayed network, Journal of Mathematical Analysis and Applications, Volume 281, Issue 2, 15 May 2003, Pages 620-632

[6] S.Guo, L.Huang, Exponential stability and periodic solutions of neural networks with continuously distributed delays, Physical Review E, 67, 011902 (2003), selected for publication in Virtual Journal of Biological Physics Research. 15 January 2003.

[7] S.Guo, L.Huang, Erratum: Exponential stability and periodic solutions of neural networks with continuously distributed delays (Physical Review E, 67, 011902, 2003). Phys. Rev. E 67, 069901(E) (2003) selected for publication in Virtual Journal of Biological Physics Research.15 June 2003.

[8] S.Guo, L.Huang, Stability analysis of a delayed Hopfield neural network, Physical Review E. 67, 061902 (2003) selected for publication in Virtual Journal of Biological Physics Research. 15 June 2003.

[9] Z.Zhang, S.Guo, Periodic Oscillation for a three -Neuron Network with Delays, Applied Mathematics Letters, Volume 16, Issue 8, November 2003, Pages 1251-1255

[10] S.Guo, L.Huang, Hopf bifurcating periodic orbits in a ring of neurons with delaysPhysica D: Nonlinear Phenomena, Volume 183, Issues 1-2, 1 September 2003, Pages 19-44

[11] S.Guo, L.Huang, Periodic solutions in an inhibitory two-neuron network, Journal of Computational and Applied Mathematics, Volume 161, Issue 1, 1 December 2003, Pages 217-229

[12] S.Guo, L.Huang, B.Dai, Z.Zhang, Global existence of periodic solutions of BAM neural networks with variable coefficients, Physics Letters A, Volume 317, Issues 1-2, 13 October 2003, Pages 97-106

[13] S.Guo, L.Huang, Convergence and periodicity in a delayed network ofneurons with threshold nonlinearity, Electronic Journal of Differential Equations. Vol. 2003(2003), No. 61, pp. 1-14.

 

 

Year 2004

[14] S.Guo, L.Huang, L.Wang, Linear stability and Hopf bifurcation in a two-neuron network with three delays, International Journal of Bifurcation and Chaos [in Applied Sciences and Engineering], Vol. 14, No. 8 (2004) 2799-2810

[15] S.Guo, L.Huang, Periodic oscillation for disrete-time Hopfield neural networks, Physics Letters A, Volume 329, Issue 3, 23 August 2004, Pages 199-206

[16] S.Guo, L.Huang, L.Wang, Exponential Stability of Discrete-Time Hopfield Neural Networks, Computers & Mathematics with Applications, Volume 47, Issues 8-9, April-May 2004, Pages 1249-1256

[17] S.Guo, L.Huang, Periodic Oscillation for a Class of Delay Difference Systems, Fields Institute Communications. 43 (2004) 177-186

 

 

Year 2005

[18] S.Guo, L.Huang, Periodic oscillation for a class of neural networks with variable coefficients Nonlinear Analysis: Real World Applications, Volume 6, Issue 3, July 2005, Pages 545-561

[19] S.Guo, L.Huang, Regular dynamics in a delayed network of two neurons with all-or-none activation functions. Physica D: Nonlinear Phenomena, Volume 206, Issues 1-2, 15 June 2005, Pages 32-48

[20] S.Guo, Spatio-temporal patterns of nonlinear oscillations in an excitatory ring network with delay, Nonlinearity, 2005, 18, 2391-2407.

[21] S.Guo, L.Huang, Global continuation of nonlinear waves in a ring of neurons, Proceedings of the Royal Society of Edinburgh: Section A, 2005, 135, 999-1015.

 

 

Year 2006

[22] S.Guo, L.Huang, Stability Analysis of Cohen-Grossberg Neural Networks, IEEE Transactions on Neural Networks, Volume 17, Number 1, January 2006, Pages 106-117.

[23] S.Guo, L.Huang, Nonlinear waves in a ring of neurons, IMA Journal of Applied Math., Volume 71, Number 4, August 2006, Pages 496-518.

 

 

Year 2007

[24] S.Guo, L.Huang, Pattern formation and continuation in a trineuron ring with delays, Acta Mathematica Sinica, Volume 35, Number 5, Pages 799-818.

[25] S.Guo, L.Huang, Stability of nonlinear waves in a ring of neurons with delays, Journal of Differential Equations, Volume 236, Number 2, Pages 343-374.

[26] S.Guo, Y. Cheng, Stability and Bifurcation of a Discrete-time Three-neuron System with Delays, International Journal of Applied Mathematics and Engineering Sciences, Volume 1, Number 1, Pages 103--115.

 

 

Year 2008

[27] X. Lu, S. Guo, Complete classification and stability of equilibria in a delayed ring network, Electronic Journal of Differential Equations, Volume 2008, No. 85, Pages 1-12..

[28] Y. Meng, S. Guo, L. Huang, Convergence dynamics of Cohen-Grossberg neural networks with continuously distributed delays, Applied Mathematics and Computation Volume 202, Pages 188-199.

[29] S. Guo, X. Tang, L. Huang, Stability and Bifurcation in a Discrete System of Two Neurons with Delays, Nonlinear Analysis Series B: Real World Applications, Volume 9, No. 4, Pages 1323--1335.

[30] S. Guo, Y. Chen, J. Wu, Bifurcations in a Delayed Network: A Case Study, Journal of Neural Computing System, Volume 1, No. 1, Pages 19--40.

[31] S. Guo, X. Tang, L. Huang, Bifurcation analysis in a discrete-time single-directional network with delays, Neurocomputing, Volume 71, No. 7-9, Pages 1422-1435.

[32] S. Guo, Y. Chen, J. Wu, Two-parameter bifurcations in a network of two neurons with multiple delays, Journal of Differential Equations, Volume 244, No. 2, Pages 444-486.

[33] S. Guo, J.S.W. Lamb, Equivariant Hopf bifurcation for Neutral Functional Differential Equations, Proceedings of the American Mathematical Society, Volume 136, No. 6, Pages 2031-2041.

 

 

Year 2009

[34] S. Guo, J.S.W. Jeroen, B. Rink, Branching patterns of wave trains in the FPU lattice, Nonlinearity Volume 22, Pages 283--299.

[35] S. Guo, Y. Yuan, Pattern Formation in a Ring Network with Delay, Mathematical Models and Methods in Applied Sciences, Volume 19, No. 10, Pages 1797-1852.

 

 

Year 2010

[36] S. Guo, Equivariant normal forms for neutral functional differential equations, Nonlinear Dynamics, Volume: 61 Issue: 1-2 Pages: 311-329 Published: 2010 .

[37] P. Zhang, S. Guo, Y. He, Dynamics of a delayed two-coupled oscillator with excitatory-to-excitatory connection, Applied Mathematics and Computation, Volume: 216 Issue: 2 Pages: 631-646 Published: 2010 .

[38] Y. Jiang, S. Guo, Linear stability and Hopf bifurcation in a delayed two-coupled oscillator with excitatory-to-inhibitory connection, Nonlinear Analysis-Real World Applications Volume: 11 Issue: 3 Pages: 2001-2015 Published: 2010.

[39] K. Xiao, S. Guo, Synchronization for two coupled oscillators with inhibitory connection, Mathematical Methods in the Applied Sciences, Volume: 33 Issue: 7 Pages: 892-903 Published: 2010 .

[40] J. Peng, S. Guo, Synchronous dynamics of two coupled oscillators with inhibitory-to-inhibitory connection, Communications in Nonlinear Science and Numerical Simulation, Volume: 15 Issue: 12 Pages: 4131-4148 Published: 2010.

 

 

Year 2011

[41] S. Guo, J. Man, Center manifolds theorem for parameterized delay differential equations with applications to zero singularities, Nonlinear Analysis-Theory Methods & Applications, Volume: 74 Issue: 13 Pages: 4418-4432 Published: 2011 .

[42] S. Guo, Y. Yuan, Delay-induced primary rhythmic behavior in a two-layer neural network, Neural Networks, Volume: 24 Issue: 1 Pages: 65-74 Published: Jan 2011 .

[43] S. Guo, Equivariant Hopf bifurcation for functional differential equations of mixed type, Applied Mathematics Letters, Volume: 24 Issue: 5 Pages: 724-730 Published: 2011 .

[44] C. Jiang, S. Guo, Y. He, DYNAMICS IN TIME-DELAY RECURRENTLY COUPLED OSCILLATORS, International Journal of Bifurcation and Chaos, Volume: 21 Issue: 3 Pages: 775-788 Published: 2011 .

[44] J. Ying, S. Guo, Y. He, Multiple periodic solutions in a delay-coupled system of neural oscillators, International Journal of Bifurcation and Chaos, Nonlinear Analysis-Real World Applications Volume: 12 Issue: 5 Pages: 2767-2783 Published: 2011.

 

 

Year 2012

[45] S. Guo, Y. Chen, J. Wu, Equivariant normal forms for parameterized delay differential equations with applications to bifurcation theory, Acta Mathematica Sinica-English Series, Volume: 28 Issue: 4 Pages: 825-856 Published: 2012.

[46] 郭上江, 吴建宏,时滞微分方程广义Hopf分岔,中国科学:数学, 42(2), pp 91-105,2012..

[47] J. Man, S. Guo, Y. He, EFFECTS OF SHORT-CUT IN A DELAYED RING NETWORK, International Journal of Bifurcation and Chaos, Volume: 22 Issue: 3 Published: 2012.

 

 

Year 2013

[48] S. Guo, J. Man, Patterns in hierarchical networks of neuronal oscillators with D-3 x Z(3) symmetry, Journal of Differential Equations Volume: 254 Issue: 8 Pages: 3501-3529 Published: 2013 .

[49] S. Guo, Zero singularities in a ring network with two delays, Zeitschrift Fur Angewandte Mathematik Und Physik Volume: 64 Issue: 2 Pages: 201-222 Published: 2013 .

[50] L. Zhang, S. Guo,Hopf bifurcation in delayed van der Pol oscillators, Nonlinear Dynamics Volume: 71 Issue: 3 Pages: 555-568 Published: 2013.