Within the framework of the Research Council on the "Cybernetics" problem at the Presidium of NAS of Ukraine since 1969 Cybernetics Department which was based on Taras Shevchenko Kyiv University started its research work. On the initiative of Academician V.M. Glushkov the Cybernetics Department established the department of complex systems modelling (CSM). The official foundation day is September 9, 1969.

The first department holder was Borys Mukolayovych Bublik, corresponding member of NAS of Ukraine, the doctor of physical and mathematical sciences, professor. Talented employees and graduates of mechanic-mathematical faculty became teachers of department: M.F. Kirichenko, O.G. Nakonechnyj, M.P. Lepeha and others. Since September, 2019 Doctor of Engineering Science, D.I. Cherniy  is a departmentholder.

Since foundation, the main specialization of the department of complex systems modelling has been the applied mathematics. The department prepared annually from 20 to 60 experts for the Academy of Sciences of Ukraine institutes and Research Studies Institutes. Over the years of department existence 22 doctors of sciences and more than 100 candidates of science have been prepared.

Main scientific achievements of the department staff are connected with the development and substantiation of numerically-analytical solution methods of mathematical physics spectral problems, theory of elasticity, plates and shells; numerical methods of research and optimal control of distributed parameter systems, in particular problem solving on the construction of optimal regulators, minimax filters, evaluation, modal control, etc. Note also deep fundamental results related to control theory: spectral theory of random matrices and limit theorems for random determinants, mathematical modeling of hydroacoustic systems, the use of locally-dimensional schemes for multidimensional optimization of distributed systems and more. On the basis of fundamental theoretical results a number of scientific results of applied nature to solve complex scientific and technical problems were obtained by the department staff. 20 monographies and over 700 journal articles were published.

The department gives a scientific seminar "Modeling and optimization of systems with incomplete data." Every two years it arranges an International Conference "Dynamical systems modelling and stability investigation". In January 2001 the department conducted an international conference "Modelling and optimization of complex systems" (MOCS, 2001), dedicated to 65th anniversary of B.M. Bublik. In 2004, together with the physical department was organized an international German-Ukrainian workshop on mathematical modeling and digital information processing, focusing on young scientists and students. The international workshop "Modeling and optimization of complex systems" (MOCS 2006), dedicated to 70th anniversary of B.M. Bublik was conducted in January 2006. From 1979 to 1990 scientific collection "Modeling and optimization of complex systems" was published.

At various times leading Ukrainian scientists from Institute of cybernetics and other scientific institutes cooperated with the department of complex systems modelling concerning scientific subjects and preparation of experts. Among them such academics as: I.M. Kovalenko, Y.M. Yermolyev, corresponding members: V.V. Skopetskyy, A.A. Chykriy, professors: V.L. Volkovych, V.L. Hirko, M. F. Kirichenko and others. Doctors of Science: M.F. Kirichenko, A.G .Nakonechny, O.F. Voloshin, V.G. Klimenko, masters of sciences: O.F. Tkalich, R.O. Soroka, M.Tsybanov, O.G. Kharchenko, N.V. Nogin, I.S. Fedorchenko, V.I. Lyashko, O.S. Slabospitsky, I.P. Kowalski, A.V. Vinogradskaya, V. A. Zaslavsky, P.M. Zinko, S.V. Volkovych, Y.M. Poznyakov, V.A. Navrodskyy, A.V. Grigorov, M. Primak, I.V. Strashnov, A.I. Stadnik , N.M. Kuzmina, E.V. Ivohin and others worked at the department at various times. Graduates of the department are heading the leading scientific institutions, departments of universities of Ukraine, all of them adequately represent the scientific school of the department of complex systems modelling.

Leading scientists of the department works as experts of the
Higher Attestation Commission of Ukraine, they are members of the specialized academic councils of the doctoral and master's theses defence.

The department maintains scientific contacts with the Yale University (New Heaven, USA), Masaryk University and the Technical University (Brno, Czech Republic), German National Research Centre of Computer Science GMD (St. Augustin, Germany), Mathematical Institute (Obervolfah, Germany).

The department of complex systems modelling will always cherish the memory of professor B.M. Bublik, M.F. Kirichenko, O.I. Nevidomsky, V.S. Mechetny, Doctor of Science B.A. Kobylyatsky.