Nikolai F. Rulkov – författare

This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium. Celebrating seminal contributions to the field by Prof. M. I. Rabinovich of the University of California at San Diego, this volume brings together perspectives on both the fundamental aspects of complexity studies, as well as in applications in different fields ranging from granular patterns to understanding of the cognitive brain and mind dynamics. The slate of world-class authors review recent achievements that together present a broad and coherent coverage of modern research in complexity greater than the sum of its parts.

This book focuses on recent progress in complexity research based on the fundamental nonlinear dynamical and statistical theory of oscillations, waves, chaos, and structures far from equilibrium.

In essence, the dynamics of real world systems (i.e. engineered systems, natural systems, social systesms, etc.) is nonlinear. The analysis of this nonlinear character is generally performed through both observational and modeling processes aiming at deriving appropriate models (mathematical, logical, graphical, etc.) to simulate or mimic the spatiotemporal dynamics of the given systems. The complex intrinsic nature of these systems (i.e. nonlinearity and spatiotemporal dynamics) can lead to striking dynamical behaviors such as regular or irregular, stable or unstable, periodicity or multi-periodicity, torus or chaotic dynamics. The various potential applications of the knowledge about such dynamics in technical sciences (engineering) are being intensively demonstrated by diverse ongoing research activities worldwide. However, both the modeling and the control of the nonlinear dynamics in a range of systems is still not yet well-understood (e.g. system models with time varying coefficients, immune systems, swarm intelligent systems, chaotic and fractal systems, stochastic systems, self-organized systems, etc.). This is due amongst others to the challenging task of establishing a precise and systematic fundamental or theoretical framework (e.g. methods and tools) to analyze, understand, explain and predict the nonlinear dynamical behavior of these systems, in some cases even in real-time. The full insight in systems’ nonlinear dynamic behavior is generally achieved through approaches involving analytical, numerical and/or experimental methods.

In essence, the dynamics of real world systems (i.e. engineered systems, natural systems, social systesms, etc.) is nonlinear. The analysis of this nonlinear character is generally performed through both observational and modeling processes aiming at deriving appropriate models (mathematical, logical, graphical, etc.) to simulate or mimic the spatiotemporal dynamics of the given systems. The complex intrinsic nature of these systems (i.e. nonlinearity and spatiotemporal dynamics) can lead to striking dynamical behaviors such as regular or irregular, stable or unstable, periodicity or multi-periodicity, torus or chaotic dynamics. The various potential applications of the knowledge about such dynamics in technical sciences (engineering) are being intensively demonstrated by diverse ongoing research activities worldwide. However, both the modeling and the control of the nonlinear dynamics in a range of systems is still not yet well-understood (e.g. system models with time varying coefficients, immune systems, swarm intelligent systems, chaotic and fractal systems, stochastic systems, self-organized systems, etc.). This is due amongst others to the challenging task of establishing a precise and systematic fundamental or theoretical framework (e.g. methods and tools) to analyze, understand, explain and predict the nonlinear dynamical behavior of these systems, in some cases even in real-time. The full insight in systems’ nonlinear dynamic behavior is generally achieved through approaches involving analytical, numerical and/or experimental methods.