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Dynamical Properties of Discrete-Time Background Neural Networks with Uniform Firing Rate

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  • Min Wan
  • Jianping Gou
  • Desong Wang
  • Xiaoming Wang

Abstract

The dynamics of a discrete-time background network with uniform firing rate and background input is investigated. The conditions for stability are firstly derived. An invariant set is then obtained so that the nondivergence of the network can be guaranteed. In the invariant set, it is proved that all trajectories of the network starting from any nonnegative value will converge to a fixed point under some conditions. In addition, bifurcation and chaos are discussed. It is shown that the network can engender bifurcation and chaos with the increase of background input. The computations of Lyapunov exponents confirm the chaotic behaviors.

Suggested Citation

  • Min Wan & Jianping Gou & Desong Wang & Xiaoming Wang, 2013. "Dynamical Properties of Discrete-Time Background Neural Networks with Uniform Firing Rate," Mathematical Problems in Engineering, Hindawi, vol. 2013, pages 1-6, April.
    • Handle: RePEc:hin:jnlmpe:892794
    DOI: 10.1155/2013/892794
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