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.