Hello everybody,

I have two paragraphs, help me to prepair them, please. Thank you very much.

1. "This paper talk about normal form of duffing-van der Pol oscillator under nonautonomous parametric perturbations. The author gave a new generalization of Poincarés normal form theory to nonautonomous differential equations applied to the Duffing-van der Pol oscillator under a nonautonomous bounded parametric perturbation. The nonautonomous normal form is calculated for parameter values corresponding to the pitchfork scenario. In this paper, the author used the computer algebra program Maple to effort accomplish the enormous computational. Finally, the author also indicate application of the normal form, which can be used to the study nonautonomous bifurcation phenomena".

2. "This paper introduced about the dichotomy spectrum for linear dunamic equations in on a time scale T (e. g. T=Z or ). This new spectrum consists of at most N closed intervals of the real line. In the autonomous cases with these intervals reduce to the real parts of the eigenvalues of A. In any cases the spectral intervals are associated with invariant vector boundles comprising solutions with a common exponential growth rate. A spectral theorem, which desribes all possible forms of the dichotomy spectrum, is the main result of this paper".

Have a nice day to you.

Hoc.

Student or Learner

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