A structural approach to control of transitional waves of nonlinear diffusion-reaction systems: Theory and possible applications to bio-medicine

Victor Kardashov, Shmuel Einav

Research output: Contribution to journalArticlepeer-review

Abstract

This paper has considered a novel approach to structural recognition and control of nonlinear reaction-diffusion systems (systems with density dependent diffusion). The main consistence of the approach is interactive variation of the nonlinear diffusion and sources structural parameters that allows to implement a qualitative control and recognition of transitional system conditions (transients). The method of inverse solutions construction allows formulating the new analytic conditions of compactness and periodicity of the transients that is also available for nonintegrated systems. On the other hand, using of energy conservations laws, allows transfer to nonlinear dynamics models that gives the possiblity to apply the modern deterministic chaos theory (particularly the Feigenboum's universal constants and scenario of chaotic transitions).

Original languageEnglish
Pages (from-to)27-40
Number of pages14
JournalDiscrete Dynamics in Nature and Society
Volume7
Issue number1
DOIs
StatePublished - 2002

Keywords

  • Density dependent diffusion
  • Finite localized transients
  • Pulse propagations chaos degree
  • Structural interaction

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