| Citation: |
Zhengxin Zhou. ON THE EQUIVALENCE OF DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 241-249. doi: 10.11948/2012017
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ON THE EQUIVALENCE OF DIFFERENTIAL SYSTEMS
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Abstract
In this article, firstly, we construct some nonlinear differential systems which are equivalent to some known systems. Secondly, we discuss the equivalence between some linear differential systems in a different method. And then we apply the obtained results to the study of the qualitative properties of these systems simultaneously.-
Keywords:
- Reflecting function /
- equivalent systems /
- periodic solutions
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References
[1] V. I. Arnold, Ordinary differential equation, Science Press, Moscow, 1971, 198-240. [2] Ph. Hartman, Ordinary differential equations, Johns Hopkins University, New York, London, Sydney, 1964. [3] S. V. Maiorovskaya, Quadratic system with linear reflecting function, Differ. Eq., 45(2) (2009), 271-273. [4] V. I. Mironenko, Reflecting function and discussion of many-dimensional differential system, Gomel University, Belarus, 2004. [5] V. V. Mironenko, Time symmetry preserving perturbations of differential systems, Differ. Eq., 40(20) (2004), 1395-1403. [6] E. V. Musafirov, Differential systems, the mapping over period for which is represented by a product of three exponential matrixes, J. Math. Anal. Appl., 329(2007), 647-654. [7] P. P. Veresovich, Nonautonomous second order quadric system equivalent to linear system, Differ. Eq., 34(12) (1998), 2257-2259. [8] Z. Zhengxin, On the Poincare mapping and periodic solutions of nonautonomous differential systems, Commun. Pure Appl. Anal., 2(6) (2007), 541-547. [9] Z. Zhengxin, The structure of reflective function of polynomial differential systems, Nonlinear Analysis, 71(2009), 391-398. -
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Citation
Zhengxin Zhou. ON THE EQUIVALENCE OF DIFFERENTIAL SYSTEMS[J]. Journal of Applied Analysis & Computation, 2012, 2(2): 241-249. doi: 10.11948/2012017
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