Wave propagation in RTD-based cellular neural networks

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This work investigates the existence of monotonic traveling wave and standing wave solutions of RTD-based cellular neural networks in the one-dimensional integer lattice Z1. For nonzero wave speed c, applying the monotone iteration method with the aid of real roots of the corresponding characteristic function of the profile equation, we can partition the parameter space (γ,δ)-plane into four regions such that all the admissible monotonic traveling wave solutions connecting two neighboring equilibria can be classified completely. For the case of c=0, a discrete version of the monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Furthermore, if γ or δ is zero then the profile equation for the standing waves can be viewed as an one-dimensional iteration map and we then prove the multiplicity results of monotonic standing waves by using the techniques of dynamical systems for maps. Some numerical results of the monotone iteration scheme for traveling wave solutions are also presented.

Original languageEnglish
Pages (from-to)339-379
Number of pages41
JournalJournal of Differential Equations
Issue number2
StatePublished - 20 Sep 2004


  • Discrete Fisher equation
  • Discrete Nagumo equation
  • Lattice dynamical systems
  • Monotone iteration methods
  • RTD-based cellular neural networks
  • Standing waves
  • Traveling waves


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