Advertisement

Dynamics of Nonlinear Parabolic Equations with Cosymmetry

  • Ekaterina S. Kovaleva
  • Vyacheslav G. Tsybulin
  • Kurt Frischmuth
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 4770)

Abstract

Dynamics of a cosymmetric system of nonlinear parabolic equations is studied to model of population kinetics. Computer algebra system Maple is applied to perform some stages of analytical investigation and develop a finite-difference scheme which respects the cosymmetry property. We present different scenarios of evolution for coexisted nonstationary regimes and families of equilibria branched off of the state of rest.

Keywords

Nonlinear Parabolic Equation Chaotic Regime Neutral Curve Variable Spectrum Oscillatory Instability 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Yudovich, V.I.: Cosymmetry, degeneration of solutions of operator equations, and the onset of filtration convection. Mat. Zametki. 49, 142–148 (1991)MathSciNetGoogle Scholar
  2. 2.
    Yudovich, V.I.: Secondary cycle of equilibria in a system with cosymmetry, its creation by bifurcation and impossibility of symmetric treatment of it. Chaos. 5, 402–411 (1995)zbMATHCrossRefMathSciNetGoogle Scholar
  3. 3.
    Murray, J.D.: Mathematical biology, p. 766. Springer, New York (1993)zbMATHGoogle Scholar
  4. 4.
    Frischmuth, K., Tsybulin, V.G.: Cosymmetry preservation and families of equilibria. In: Computer Algebra in Scientific Computing – CASC 2004, pp. 163–172 (2004)Google Scholar
  5. 5.
    Frischmuth, K., Tsybulin, V.G.: Families of equilibria and dynamics in a population kinetics model with cosymmetry. Physics Letters A 338, 51–59 (2005)zbMATHCrossRefGoogle Scholar
  6. 6.
    Govorukhin, V.N.: Calculation of one-parameter families of stationary regimes in a cosymmetric case and analysis of plane filtrational convection problem. Continuation methods in fluid dynamics, Notes Numer. Fluid Mech. Vieweg. Braunschweig 74, 133–144 (2000)MathSciNetGoogle Scholar
  7. 7.
    Frischmuth, K., Tsybulin, V.G.: Computation of a family of non-cosymmetrical equilibria in a system of two nonlinear parabolic equations. Computing 16, 67–82 (2002)MathSciNetGoogle Scholar
  8. 8.
    Yudovich, V.I.: Bifurcations under perturbations violating cosymmetry. Doklady Physics 49(9), 522–526 (2004)CrossRefMathSciNetGoogle Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2007

Authors and Affiliations

  • Ekaterina S. Kovaleva
    • 1
  • Vyacheslav G. Tsybulin
    • 1
  • Kurt Frischmuth
    • 2
  1. 1.Department of Computational Mathematics, Southern Federal University, Rostov-na-DonuRussia
  2. 2.Department of Mathematics, University of RostockGermany

Personalised recommendations