Contents V.12 N.2.2021

  • ASYMPTOTIC REDUCTION OF SOLUTION SPACE DIMENSION FOR DYNAMICAL SYSTEMS
    PAVEL S. PANKOV , ZHUMAGUL K. ZHEENTAEVA , TALEH SHIRINOV (pp. 243-253)
  • Abstract.

    We introduce the equivalence relation in the solution space to initial value problem for dynamical systems: the distance between their trajectories approaches zero with time approaching infinity. The phenomenon ”the dimension of the quotient space is less than one of the initial spaces” is named ”asymptotic reduction of solution space dimension”. We demonstrate that various well-known results including existence of special solutions of delay differential equations with small argument can be presented uniformly by this method. These results are extended to operator-difference equations and improved by the new method of splitting spaces. Some results are further verified by computations.

    Keywords:

    difference equation, delay differential equation, asymptotic, quotient space, special solution.

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