Martynyuk is organizer and head of the Department of Processes Stability at the S.P. Timoshenko Institute of Mechanics of the National Academy of Sciences of Ukraine (NAS of Ukraine) since 1978.  

He developed the method of Lyapunov matrix functions as applied to uncertain systems, systems with fuzzy information, and dynamic equations on time scales, non-classical theories of stability of motion, chaotic dynamics, and mathematical ecology. 

As the editor of a series of scientific monographs "Stability and Control: Theory, Methods and Applications" (1995-2002) at the publishing house Gordon and Breach (UK) and Taylor and Francis (USA) he organized the work of scientists from many countries of the world to create the series consist with 22 volumes, which opened new opportunities for young scientists to continue research in many areas of research in the qualitative theory of equations. 

He is currently focusing on the publication of a series of scientific monographs "Stability, Oscillation and Optimization of Systems" at the publishing house Cambridge Scientific Publishers (UK). 

Martynyuk is the founder and editor-in-chief of the International Scientific Journal "Nonlinear Dynamics and Systems Theory", which is well known throughout the world. 

He is the author (co-author) of a number of monographs in Russian, English and Chinese. 

He is a doctor of physical and mathematical sciences, professor, academician of the NAS of Ukraine, laureate of the State Prize of Ukraine in the field of science and technology. 

Martynyuk is based in Ukraine, but he actively communicates with experts from all over the world that are interested in stability theory and motion control in the study of real-world phenomena.