Existence of monotonic traveling waves in lattice dynamical systems

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This paper deals with the existence of monotonic traveling and standing wave solutions for a certain class of lattice differential equations. Employing the techniques of monotone iteration coupled with the concept of upper and lower solutions in the theory of monotone dynamical systems, we can classify the monotonic traveling wave solutions with various asymptotic boundary conditions. For the case of zero wave speed, a novel discrete monotone iteration scheme is established for proving the existence of monotonic standing wave solutions. Applications are made to several models including cellular neural networks, original and modified RTD-based cellular neural networks. Numerical simulations of the monotone iteration schemes are also given.

Original languageEnglish
Pages (from-to)2375-2394
Number of pages20
JournalInternational Journal of Bifurcation and Chaos in Applied Sciences and Engineering
Issue number8
StatePublished - Aug 2005


  • Cellular neural networks
  • Lattice dynamical systems
  • Monotone iteration methods
  • Standing waves
  • Traveling waves


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