The adjoining cell mapping and its recursive unraveling, part II: Application to selected problems

Abstract

Several applications of the adjoining cell mapping technique are provided here by employing the adaptive mapping unraveling algorithm to analyze smooth and pathological autonomous dynamical systems. The performance of an implementation of recursive unraveling algorithm is also illustrated regarding its low memory requirements for computational purposes when compared with the simple cell mapping method. The applications considered here illustrate the effectiveness of the adjoining cell mapping technique in its ability to determine limit cycles and to unravel nonstandard dynamics. The advantages of this new technique of global analysis over the simple cell mapping method are discussed.

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Guttalu, R.S., Zufiria, P.J. The adjoining cell mapping and its recursive unraveling, part II: Application to selected problems. Nonlinear Dyn 4, 309–336 (1993). https://doi.org/10.1007/BF00120669

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Key words

  • Nonlinear autonomous dynamical systems
  • simple cell mapping
  • limit cycles
  • adjoining cell mapping
  • adaptive integration
  • recursive algorithms