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The reduction principle is a common idea which states that while researching the stability of solutions of the dynamic system (the system of differential, difference, differential-difference equations) the order of the researched system can be decreased. As the main obstacle in researching a dynamic system is a big dimension of the system, decreasing the order significantly simplifies the stability of the research process.
This work contains some ways of decreasing the system order. The author aimed to keep the details to a minimum, to facilitate a better understanding of the main ideas, and the rigor of explanations is replaced by examples and references to the original works.
The project Modern Mathematics for Engineers is addressed to upper-course University students in Mathematics specialties, to graduate students and to researchers who apply Mathematics in different spheres.

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Dr. Tamara G. Stryzhak is Professor of Mathematics at the Department of Higher Mathematics of the National Technical University of Ukraine, Kiev Polytechnical Institute , and the Secretary of the Ukrainian National Committee of IAESTE. She studied at the National Taras Shevchenko University of Kiev, and defended her Candidate of Science thesis at the Institute of Mathematics of the USSR Academy of Sciences as well as her Doctor of Science dissertation at the Novosibirsk Section of the USSR Academy of Sciences. She is the author of five monographs, three textbooks, and more than 200 articles in mathematical journals.

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