Mathematical methods in modern complexity science This book presents recent developments in nonlinear and complex systems. It provides recent theoretic developments and new techniques based on a nonlinear dynamical systems approach that can be used to model and understand complex behavior in nonlinear dynamical systems. It covers information theory relativistic chaotic dynamics data analysis relativistic chaotic dynamics solvability issues in integro differential equations and inverse problems for parabolic differential equations synchronization and chaotic transient. Presents new concepts for understanding and modeling complex systems. Preface Shannon Information Analysis of the Chromosome Code. An Unfair Coin of the Standard & Poor’s 500 Relativistic chaotic scattering Artificial Intelligence for Studying Perception of Ambiguous Images and Decision Marking Processes in the Human BrainMultistability Coexistence of Memristive Chaotic System and the Application in Image Decryption Extreme Events and Emergency Scales Evolution of Systems with Power Law Memory: Do We Have to Die Probability Entanglement and Destructive Interference in Biased Coin Tossing On the solvability of some systems of integro diﬀerential equations with drift. Solvability in The Sense of Sequences For Some Non Fredholm Operators With The Bi Laplacian The Preservation of Nonnegativity of Solutions of A Parabolic System With The Bi Laplacian Inverse problems for some systems of parabolic equations with coefﬁcient depending on time.