Analytical and Computational Modeling of Complex Systems

A Systematic Approach to Understanding Real-World Complexity
Erscheinungsjahr 2027
ISBN: 978-0-443-52669-5
Verlag: Elsevier Science

Buch, Englisch, 250 Seiten, Format (B × H): 191 mm x 235 mm

Analytical and Computational Modeling of Complex Systems: A Systematic Approach to Understanding Real-World Complexity presents modern studies of complex systems by methods of statistical physics, numerical calculation, and computer modeling. Using general methods of investigating the branching (bifurcations) of solutions for nonlinear equations, the authors present an exhaustive analysis of the order parameter dependences on the control parameter in a small vicinity of the equilibrium values of parameters, including the stability analysis of the equilibrium states, and the asymptotic behavior of the order parameter dependences on the control parameter (bifurcation diagrams). The authors also present concepts and techniques used to model heterogeneous multi-agent interactions, complex neural networks, biochemical reaction networks in cells, and the dynamic behavior of economic systems over time. The book serves as both a learning resource and a practical reference for those engaged in the study of complex systems and their diverse real-world implementations. The book also offers a systematic learning path from theory to applications. It provides case studies that bridge the gap between mathematical formalism and complex systems modeling and simulation. Emphasizing hybrid and probabilistic modeling techniques, the book ensures greater flexibility for real-world applications. Covering a broad range of topics, it supports interdisciplinary use across departments such as physics, computer science, engineering, economics, and more.

Autoren/Hrsg.

Paladi, Florentin

Barsuk, Alexandr A.

Aybar, Orhan Özgür

Aybar, Ilknur Kusbeyzi

Fachgebiete

• Mathematik | Informatik Mathematik Mathematik Allgemein Diskrete Mathematik, Kombinatorik
• Wirtschaftswissenschaften Betriebswirtschaft Unternehmensforschung
• Mathematik | Informatik EDV | Informatik Business Application Unternehmenssoftware
• Mathematik | Informatik Mathematik Mathematische Analysis Differentialrechnungen und -gleichungen
• Mathematik | Informatik EDV | Informatik Programmierung | Softwareentwicklung Algorithmen & Datenstrukturen

Inhaltsverzeichnis

1. Introduction and Conceptual Foundations
2. Bifurcation and Stability Analysis of Equilibrium States in Complex Thermodynamic Systems Near Equilibrium Parameter Values
3. Sensitivity Analysis of Equilibrium States in Multi-Dimensional Dynamical Systems Near Ordinary and Bifurcation Parameter Values
4. General Solution for Phase Transitions Involving an Intermediate Metastable State
5. Unified Probabilistic Framework for Modeling Complex Adaptive Populations
6. Neuronal Dynamics and Information Processing. From Single Neurons to Network Behavior
7. Biochemical Reaction Networks. Mathematical Modeling of Cellular Processes
8. Economic Motion in Mathematical Time. From Cycles to Chaos
9. From Theory to Data. Empirical Methods for Economic Dynamical Systems
10. Summary and Future Directions

Über Autor(innen)

Aybar, Ilknur Kusbeyzi
Dr. Ilknur Kusbeyzi Aybar, Yeditepe University, Department of Mathematics, Istanbul, Türkiye. Ilknur Kusbeyzi Aybar is Ph.D., associate professor in the Department of Mathematics at Yeditepe University. She has been a faculty member at Yeditepe University since 2005, serving in various academic and administrative roles, and was promoted to associate professor position in February 2022. She earned her Ph.D. in Mathematics from Gebze Technical University in 2010, following undergraduate and master’s studies at Yildiz Technical University. Dr. Ilknur Kusbeyzi Aybar’s research focuses on the mathematical modeling and qualitative analysis of nonlinear dynamical systems, with particular emphasis on bifurcation and chaos theory, stability analysis, and symbolic computation in differential equations and polynomial systems. Her interdisciplinary interests extend to mathematical biology, neuronal dynamics, and chemical reaction modeling. Dr. Ilknur Kusbeyzi Aybar serves as head of the Department of Mathematics at Yeditepe University.

Aybar, Orhan Özgür
Dr. Orhan Özgür Aybar, Piri Reis University, Institute of Graduate Education - Computational Science and Engineering, Istanbul, Türkiye. Orhan Özgür Aybar is Ph.D., associate professor in the Department of Mathematics and Management Information Systems at Piri Reis University, where he has served since 2014 and was promoted to associate professor position in February 2024. He earned his Ph.D. in Mathematics from Gebze Institute of Technology in March 2014, following degrees in Physics with Computational Physics specialization from Bogazici University in Istanbul. Dr. Aybar’s research focuses on nonlinear dynamical systems, bifurcation theory, and stability analysis of differential equations and polynomial systems. His computational science contributions include developing algorithms for computer algebra systems to analyse biochemical reaction networks, implementing genetic algorithm approaches for chaotic system analysis, and creating symbolic computation methods for bifurcation detection in complex dynamical systems. Dr. Orhan Özgür Aybar serves as director of the Institute of Graduate Education and leads the Department of Computational Science and Engineering.

Paladi, Florentin
Dr. Florentin Paladi, Moldova State University, Department of Theoretical Physics, Chisinau, Moldova. Florentin Paladi is D.Sc., professor and former dean of the Faculty of Physics and Engineering and vice-rector for research at the Moldova State University (2012-2021). He earned a BSc diploma with distinction in Physics from Moldova State University in 1993, Ph.D. in Theoretical and Mathematical Physics in 1996, Doctor of Philosophy diploma in 1997, and D.Sc. in Physics and Mathematics in 2010. Laureate of the State Prize for outstanding young scientists in 1998. During the period of 1998-2002 he held a postdoctoral research position at the Tokyo Institute of Technology in Japan. In 2020 he founded the research laboratory Environmental Physics and Modeling Complex Systems. A Fulbright research scholar at the Centre for the Study of Complex Systems of the University of Michigan in Ann Arbor and research projects at the Brunel University in London and the University of Missouri in Columbia. He is Laureate of the Academy of Sciences of Moldova Award for the valuable scientific achievements of scientists in the natural and exact sciences for the development of analytical and numerical methods in complex systems research.

Barsuk, Alexandr A.
Dr. Alexandr A. Barsuk, Moldova State University, Institute of Applied Physics, Chisinau, Moldova. Alexandr A. Barsuk is D.Sc., professor and principal scientific researcher in the research laboratory Environmental Physics and Modeling Complex Systems of the Institute of Applied Physics at the Moldova State University. Former head of the Computing Centre of the Moldova State University. D.Sc. in Physics and Mathematics from Tula State University in 1998. Research projects on analytical methods in structural mechanics and theoretical physics, variational and numerical analysis of stability of deformable bodies, and asymptotic analysis of complex systems. He is co-author of Stability of Axially Moving Materials (2020), part of the Springer Nature book series in Solid Mechanics and Its Applications. Prof. A.A. Barsuk is Laureate of the Ministry of Education and Research Award for his prodigious activity in the field of research and innovation.