Anatoly A. Martynyuk was born in the family of a railway mechanics, Andrey Gerasimovich Martynyuk, who lived in the Cherkassky region of UkrSSR (since 1991 Ukraine). After graduating from Physical and Mathematical Department of B. Khmelnitsky State University of Cherkassy he entered the post-graduate school supervised by Professor A.N. Golubentsev at the Institute of Mechanics of Academy of Science of Ukr.SSR (now the S.P. Timoshenko Institute of Mechanics of National Academy of Sciences of Ukraine) and focused on problems of finite stability on a given time interval. Three years later Martynyuk conducted research and published several papers with a new approach for an estimation of finite stability of motion on a given time interval (practical stability). The above problems were treated by such renowned scientists as N.D. Moiseyev, N.G. Chetayev and others. In spite of this challenge, Martynyuk obtained new qualitative results.
Along with these investigations and those included in his Doctoral Thesis (which he defended in 1973), Martynyuk developed foundations of motion stability theory for large scale dynamical systems with non-asymptotically stable subsystems. In 1978, he founded the Department of Processes Stability at the Institute of Mechanics of Academy of Sciences of Ukr.SSR, and he has been its Head ever since. Among other activities at the Department of Processes Stability, Martynyuk chaired the Seminar ''Stability Theory and its Applications'' during which various new results obtained by Ukrainian and European scholars were discussed. In 2009, Martynyuk was elected the Full Member of the National Academy of Science of Ukraine. In 2008, he was awarded a National Prize in the field of Science and Technology.
The main scientific results obtained by Martynyuk were as follows:
Alongside his prolific scientific research, Martynyuk has been involved in very intense scientific-organizational and publishing activities. In 1982, he organized publication of the book ''Lectures on Theoretical Mechanics'' by A.M. Lyapunov. He also made an ample amount of work as the editor of the International Series of Scientific Monographs ''Stability and Control: Theory, Methods and Applications'' copyrighted by the Gordon and Breach Science Publishers (Great Britain). From 1992 to 2002 they published 22 volumes in the Series which gained in a worldwide recognition.
In 2001 Martynyuk founded the International Academic Journal of ''Nonlinear Dynamics and Systems Theory'' and its online version at http://e-ndst.kiev.ua and he has been its chief editor.
In 2006 he established a new International Series of Scientific Monographs, Textbooks and Lecture Courses entitled ''Stability, Oscillations and Optimization of Systems'' at the Cambridge Scientific Publishers and is serving as its chief editor. By now, 8 volumes of the Series have appeared.
Martynyuk is an editorial board member of three Russian-language journals: the International Journals of ''Applied Mechanics'', ''Nonlinear Oscillations'' and ''Electronic Modeling'' and two English-language journals: ''Journal of Applied Mathematics and Stochastic Analysis'' (USA) and ''Differential Equations and Dynamical Systems'' (India).
Martynyuk has been a major advisor to 27 Candidates (Ph.D.) and 3 Doctors (Habilitation) in Physical and Mathematical Sciences who are now employed and are being successful workers in various countries of the former Soviet Union. He is a member of several Scientific Councils on awarding scientific degrees of Candidate (Ph.D.) and Doctor (Habilitation) of Physical and Mathematical Sciences. Martynyuk is a vice-president of the National Committee on Theoretical and Applied Mechanics of Ukraine.