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Global consensus for discrete-time competitive systems

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  • Shih, Chih-Wen
  • Tseng, Jui-Pin

Abstract

Grossberg established a remarkable convergence theorem for a class of competitive systems without knowing and using Lyapunov function for the systems. We present the parallel investigations for the discrete-time version of the Grossberg’s model. Through developing an extended component-competing analysis for the coupled system, without knowing a Lyapunov function and applying the LaSalle’s invariance principle, the global pattern formation or the so-called global consensus for the system can be achieved. A numerical simulation is performed to illustrate the present theory.

Suggested Citation

  • Shih, Chih-Wen & Tseng, Jui-Pin, 2009. "Global consensus for discrete-time competitive systems," Chaos, Solitons & Fractals, Elsevier, vol. 41(1), pages 302-310.
    • Handle: RePEc:eee:chsofr:v:41:y:2009:i:1:p:302-310
    DOI: 10.1016/j.chaos.2007.12.005
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    References listed on IDEAS

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