Global consensus for discrete-time competitive systems

Chih-Wen Shih and Jui-Pin Tseng

Chaos, Solitons & Fractals, 2009, vol. 41, issue 1, 302-310

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.

Date: 2009
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:41:y:2009:i:1:p:302-310

DOI: 10.1016/j.chaos.2007.12.005

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