From Newton's Second Law to the Decoding of Complex Fluctuations

This book introduces the latest results of interdisciplinary research on complex systems. Dr. He Zonglu obtained the nonlinear autoregressive integrated (NLARI) model for describing complex systems by mathematizing Newton's second law in stochastic systems. The NLARI model clarifies the generative mechanism and regulatory mechanism of complex systems (open systems feedback loops system evolution randomness nonlinearity fractality and adaptability). In particular nonlinear dynamical behavior and fractal behavior arise from the same physical integer-dimensional topological space the former depending on the restoring and resisting forces within the system and the latter as a product of fluctuations which are the system's response to external perturbations. Self-adaptive functions are the product of maintaining stable fixed points through the resilience of Gaussian function component with the resistance. Separate complementary modeling of networks emergence spontaneous order and self-organizing behavior. Applied results include SSCCPI circuits for efficient temporal signal propagation of high-intensity information in cortical networks heart rate/heart rate variability for identifying heart disease and predicting the risk of sudden cardiac death and optimal pathway for economic growth. This book demonstrates that the optimal way to increase profits at von Neumann equilibrium prices is achieved by a dynamic equilibrium-stabilizing fixed point formed by market competition and that the ratio of average investment to economic resistance coefficient determines the rate of economic growth. NLARI model-based approach standardizes the research methodology in the field of complex systems. The methodology is highly interpretable since all parameters are derived mathematically have the same dynamical meaning and different physical meaning. The book details modeling parameter estimation statistical tests algorithms prediction simulation and interpretation of results and phenomena and provides examples of applications in biology network theory medicine and economics. This book is applicable to the study of complexity in a wide range of fields.