Research interests

Plykin attractor on the 2D-sphere

  • Realization of abstract models and phenomena of nonlinear dynamics
  • Two-parameter analysis of nonlinear systems. Atlas of charts of dynamical regimes
  • Critical dynamics at the onset of chaos and renormalization group.
  • Quasiperiodic dynamics and strange nonchaotic attractors.
  • Coupled map lattices.
  • Complex analytic maps and their application to physical systems.
  • Quantum chaos.
  • Transitions to chaos in presence of noise.
  • Numerical algorithms for nonlinear dynamics.
  • Systems with catastrophes.
  • Complex dynamics of spatially extended systems.
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    Atlas of Charts of Dynamical Regimes

    Equations of dynamical systems often contain parameters, the constant quantities determining character of observing regimes. In the case of two control parameters there exists a useful visual representation of the system behavior by means of charts of dynamical regimes - diagrams on the parameter plane where domains of qualitatively distinct regimes are indicated by colors.

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    Personal sceintific results

    Here the links are collected pointing the pages created by scientists of our group, that are related to the personal scientific results and to the adjacent problems.

    Saratov group
    of theoretical nonlinear