Dr. Stojanović currently holds an Associate Professor position at the Faculty of Mechanical Engineering, University of Niš, Serbia, and a Visiting Professor position at Lakehead University, Ontario, Canada. Since 2011, he has published numerous papers in prestigious scientific journals, where he also serves as a reviewer. As an internationally recognized scientist, he has been invited to lecture at universities worldwide and has participated in the most significant conferences in the field of theoretical and applied mechanics. His research interests primarily focus on the modeling of complex linear and nonlinear continuous and discrete dynamical systems, analytical and numerical methods for solving MDOF-based models, and the application of dynamic and stochastic stability principles to engineering problems in vibration. Dr. Deng is currently Chair and Associate Professor in the Department of Civil Engineering at Lakehead University, Canada. He is a licensed professional engineer in Ontario and has over 20 years of research, education, and industry experience. Dr. Deng’s research group is developing theories and techniques to better understand dynamic instability, geohazards, and the reliability of structures in civil and mining engineering, especially in geotechnical engineering. His excellence in research has been recognized through several awards, including the Best Paper Award, the Research Excellence Award, and the Best Presentation Award. These accolades underscore the impact of Dr. Deng’s guidance and contributions to both research excellence and student development. Dr. Petković received a PhD in Computer Science in 2008 from the University of Niš, Serbia. He is a prolific author, the editor-in-chief of the Facta Universitatis, Series: Mathematics and Informatics, and section editor for three other recognized journals. He is the author of more than 15 software solutions, both commercial and non-commercial scientific software. His research interests include numerical linear algebra, neural networks, source and channel coding, and optimization methods. Marko A. Ristić received his MSc degree in Mechanical Design and Mechanization in 2009 from the University of Niš. Currently, he works as a Researcher at the Faculty of Mechanical Engineering, University of Niš, to complete his doctoral thesis. His research interests include machine component design, finite element analysis, computational fluid dynamics, gear design, planetary gear trains, and high-conformal gearing.

• Part I: Fundamental mathematical background of dynamics and vibrations: Overview of numerical methods and recent improvements1. Mathematical methods and procedures in the analysis of stability of vibrations of complex moving objects2. Mathematical methods and applications in the analysis of nonlinear vibrations3. Mathematical methods in stochastic stability of mechanical systemsPart II: Stability of vibrations of complex moving objects: Modeling and applications4. Stabilization and critical velocity of a moving mass5. Stability of vibration of a complex discrete oscillator moving at an overcritical speed6. Vibrational benefits of a new stabilizer in moving coupled vehicles7. Dynamics and stability of a complex rail vehicle system8. Modeling of a three-part viscoelastic foundation and its effect on dynamic stability9. Vibrational instability in a complex moving object: Innovative approaches to elastically damped connections between car body components and supportsPart III: Nonlinear vibrations: Stabilizing phenomena and applications10. Nonlinear amplitude analysis of shear deformable beams supported by an elastic foundation with variable discontinuity11. Nonlinear vibrational characteristics of damaged beams resting on a Pasternak foundation12. The purpose of an arch in the stability of nonlinear vibrations of coupled structures13. Quantitative effect of an axial load on the amplitude stability of rotating nano-beams14. Coupled multiple plate systems and their stability characteristicsPart IV: Stochastic stability of structures and mechanical systems: Methodology and examples15. Moment Lyapunov exponents and stochastic stability of vibrationally isolated laminated plates16. Higher-order stochastic averaging method in fractional stochastic dynamics17. Parametric stochastic stability of viscoelastic rotating shafts18. Stochastic stability of circular cylindrical shells19. Generalized transformations for MDOF stochastic systemsPart V: From traditional methods to Artificial Intelligence20. Modeling and applications of markers in machine learning and technical practice