Science in China Series A: Mathematics

, Volume 44, Issue 2, pp 193–200 | Cite as

Chaos and asymptotical stability in discrete-time recurrent neural networks with generalized input-output function

  • Jinliang Wang
  • Luonan Chen
  • Zhujun Jing


We theoretically investigate the asymptotical stability, local bifurcations and chaos of discrete-time recurrent neural networks with the form of
$$u_i \left( {t + 1} \right) = ku_i \left( t \right) + \Delta t\left( {\sum\limits_{j = 1}^n {a_{ij} v_j \left( t \right) + a_i } } \right), i = 1,2, \cdots ,n,$$
, where the input-output function is defined as a generalized sigmoid function, such asv i =2/π arctan(π/2μiμi),\(v_i = \frac{2}{\pi }arctan\left( {\frac{\pi }{2}\mu _i u_i } \right)\) and\(v_i = \frac{1}{{1 + e^{ - u_i /\varepsilon } }},\), etc. Numerical simulations are also provided to demonstrate the theoretical results.


chaos asymptotical stability bifurcation neural network snap-back repeller 


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Copyright information

© Science in China Press 2001

Authors and Affiliations

  • Jinliang Wang
    • 1
  • Luonan Chen
    • 2
  • Zhujun Jing
    • 1
    • 3
  1. 1.Institute of MathematicsChinese Academy of SciencesBeijingChina
  2. 2.Osaka Sangyo UniversityOsakaJapan
  3. 3.Department of MathematicsHunan Normal UniversityChangshaChina

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