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The paper deals with the stability and the bifurcation of a class of inertial neural networks. Based on sensitivity theory, we determine the suitable bifurcation parameter. Using Routh-Hurwitz criterion and bifurcation theory, we give some new criteria for stability,Hopf bifurcation and steady state bifurcation. Numerieal simulations are given to validate the theoretieal analysis showing that the delayed feedback controller can control the occurrence of bifurcation effectively and the amplitude of the bifurcated limit cycle as well.
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Keywords:
- inertial neural networks /
- stability /
- delayed feedback controller /
- Hopf bifurcation
[1] Hopfield J 1982 Proc.Nat.Acad. Usa 79 2554
[2] Chua L, Yang L 1988 IEEE Trans. Circuits Systems 35 1257
[3] Xu D, Zhao H 2001 Comput. Math. Appl. 42 39
[4] Wu R, 2009 Acta Phys. Sin. 58 0139(in Chinese)[吴然超 2009 58 0139]
[5] Ji Y, Cui B 2010 Chin. Phys. B 19 060512
[6] Wang L, Xu D 2003 Science in China E 6 488 (in Chinese) [王林山、徐道义2003中国科学 E 6 488]
[7] Chen D, Zhang W 2008 Chin. Phys. B 17 1506
[8] Zhao H, Sun L, Wang G 2007 Neurocomputing 70 292
[9] Zhao H, Wang L 2007 Nonlinear Analysis 8 73
[10] Lou Y, Cui B 2008ActaPhys. Sin. 57 2060(in Chinese)[楼旭阳、崔宝同 2008 57 2060]
[11] Wheeler D,Schieve W 1997 Physica D 105 267
[12] Li C, Chen G, Liao X 2004 The European Physical Journal B 41 337
[13] Liao X,Li S 2003 Nonlinear Dynamics 33 209
[14] Liu Q,Liao X 2009 Nonlinear Analysis 10 2384
[15] Yang X,Yang F 2004 Chaos,Solitons and Fractals 20 587
[16] Khalil H 1996 Nonlinear Systems (NJ:Prentice Hall)
[17] Zhang L, Zhang C 2009 Mathematica Applicata 22 452(in Chinese)[张 岚、张诚坚 2009 应用数学 22 452]
[18] Hassard B, Kazarinoff N 1981 Theory and Application of Hopf bifurcation (Cambridge University Press, Cambridge).
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[1] Hopfield J 1982 Proc.Nat.Acad. Usa 79 2554
[2] Chua L, Yang L 1988 IEEE Trans. Circuits Systems 35 1257
[3] Xu D, Zhao H 2001 Comput. Math. Appl. 42 39
[4] Wu R, 2009 Acta Phys. Sin. 58 0139(in Chinese)[吴然超 2009 58 0139]
[5] Ji Y, Cui B 2010 Chin. Phys. B 19 060512
[6] Wang L, Xu D 2003 Science in China E 6 488 (in Chinese) [王林山、徐道义2003中国科学 E 6 488]
[7] Chen D, Zhang W 2008 Chin. Phys. B 17 1506
[8] Zhao H, Sun L, Wang G 2007 Neurocomputing 70 292
[9] Zhao H, Wang L 2007 Nonlinear Analysis 8 73
[10] Lou Y, Cui B 2008ActaPhys. Sin. 57 2060(in Chinese)[楼旭阳、崔宝同 2008 57 2060]
[11] Wheeler D,Schieve W 1997 Physica D 105 267
[12] Li C, Chen G, Liao X 2004 The European Physical Journal B 41 337
[13] Liao X,Li S 2003 Nonlinear Dynamics 33 209
[14] Liu Q,Liao X 2009 Nonlinear Analysis 10 2384
[15] Yang X,Yang F 2004 Chaos,Solitons and Fractals 20 587
[16] Khalil H 1996 Nonlinear Systems (NJ:Prentice Hall)
[17] Zhang L, Zhang C 2009 Mathematica Applicata 22 452(in Chinese)[张 岚、张诚坚 2009 应用数学 22 452]
[18] Hassard B, Kazarinoff N 1981 Theory and Application of Hopf bifurcation (Cambridge University Press, Cambridge).
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