Aleksandr A. Barsuk – författare

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 modelling. 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 behaviour of the order parameter dependences on the control parameter (bifurcation diagrams). The existence of five canonical (normal) forms of bifurcations is shown, and the role of the intermediate metastable state in the kinetics of phase transitions is elucidated in the framework of these parametric models. The modelling is extended to multi-dimensional dynamical systems. Relations between the infinitesimal quantities of order parameters and the control of dynamical systems are given, and the formulae for the order parameter sensitivity are presented, depending on the variations in the control parameters. Stability analysis of the equilibrium states for nonlinear complex systems described by the Landau-type kinetic potential with two order parameters and the Lotka-Volterra model is conducted. Two different rate processes as combinations of in series and in parallel pathways are described. The peculiarities of the anomalous generation and extinction phenomenon of crystal nuclei at very low temperatures in non-equilibrium supercooled liquids are presented. Also, a robust methodology is applied to heterogeneous complex systems with stochastic interactions to optimize the distribution of particles among clusters, based on both the total number of particles in the system and the number of available states. In addition, the book presents an integrated approach that bridges stochastic modelling with computational agent-based models. Building on this foundation, the authors then introduce a unified probabilistic framework for modelling heterogeneous multi-agent interactions in complex systems that exhibit memory and adaptive learning. This approach (which appears phenomenological if it is not agent-based) can precisely describe the average outcomes of agent-based computations (where there is a lack of probabilistic insight). Developing such a framework, unlike conventional agent-based models, maintains analytical tractability through mean-field approximations, while capturing complex emergent behaviors. Models are validated using diverse real-world applications. The book also presents concepts and techniques used to model complex neural networks, biochemical reaction networks in cells, and the dynamic behaviour of economic systems over time. By balancing theoretical depth with intuitive explanations and practical applications, this 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.Introduces a coherent methodology that integrates analytical techniques with probabilistic and computational approaches for modeling complex adaptive populations and dynamical systems, and offers real-world applications ranging from the physics of phase transitions and ecology to cellular processes and economic dynamical systemsPresents techniques for analysis of bifurcations and stability in complex thermodynamic systems near equilibrium parameter values, sensitivity analysis of equilibrium states in multi-dimensional dynamical systems, including general solution for phase transitions involving an intermediate metastable stateHelps readers develop transferable skills in system analysis, regardless of domain, and provides a dual approach that accommodates a wider audience, from mathematically oriented researchers to practitioners seeking applicable computational toolsApplied case studies and examples Include MATLAB and Python program code, along with their outputs, tables, and figures