Nonlinear dynamics of chaotic and stochastic systems

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This improved and enlarged edition of our previous work on nonlinear dynamics of chaotic and stochastic systems builds upon the original published in 2002. The new edition includes clarifications in several sections and corrections of misprints in formulas. Notably, three new sections have been added to Chapter 2: "Statistical Properties of Dynamical Chaos," "Effects of Synchronization in Extended Self-Sustained Oscillatory Systems," and "Synchronization in Living Systems." These additions reflect significant findings by the authors since the first edition's release. We aim for this edition to engage a broad audience, from specialists to newcomers in nonlinear oscillation and wave theory, dynamical chaos, synchronization, and stochastic process theory. The book explores both classical foundations and contemporary results in nonlinear dynamics, emphasizing the effects of noise on various dynamic regimes and the emergence of order through noise. While there is a wealth of literature on nonlinear dynamics and chaos, as well as on statistical physics of far-from-equilibrium processes, this book seeks to merge deterministic nonlinear dynamics with statistical physics approaches, highlighting the critical role of noise in shaping the dynamics of nonlinear dissipative systems.