Complexity, Emergent Systems and Complex Biological Systems:\ud Complex Systems Theory and Biodynamics. [Edited book by I.C. Baianu, with listed contributors (2011)]

An overview is presented of System dynamics, the study of the behaviour of complex systems, Dynamical system in mathematics Dynamic programming in computer science and control theory, Complex systems biology, Neurodynamics and Psychodynamics.\u

Introduction to the Modeling and Analysis of Complex Systems

Keep up to date on Introduction to Modeling and Analysis of Complex Systems at http://bingweb.binghamton.edu/~sayama/textbook/! Introduction to the Modeling and Analysis of Complex Systems introduces students to mathematical/computational modeling and analysis developed in the emerging interdisciplinary field of Complex Systems Science. Complex systems are systems made of a large number of microscopic components interacting with each other in nontrivial ways. Many real-world systems can be understood as complex systems, where critically important information resides in the relationships between the parts and not necessarily within the parts themselves. This textbook offers an accessible yet technically-oriented introduction to the modeling and analysis of complex systems. The topics covered include: fundamentals of modeling, basics of dynamical systems, discrete-time models, continuous-time models, bifurcations, chaos, cellular automata, continuous field models, static networks, dynamic networks, and agent-based models. Most of these topics are discussed in two chapters, one focusing on computational modeling and the other on mathematical analysis. This unique approach provides a comprehensive view of related concepts and techniques, and allows readers and instructors to flexibly choose relevant materials based on their objectives and needs. Python sample codes are provided for each modeling example. This textbook is available for purchase in both grayscale and color via Amazon.com and CreateSpace.com.https://knightscholar.geneseo.edu/oer-ost/1013/thumbnail.jp

Proceedings of AUTOMATA 2010: 16th International workshop on cellular automata and discrete complex systems

International audienceThese local proceedings hold the papers of two catgeories: (a) Short, non-reviewed papers (b) Full paper

Systems evolution: the conceptual framework and a formal model

This research addresses to some of the fundamental problems in systems science.T he aim of this study is to: (1) provide a general conceptual framework for systems evolution; (2) develop a formal model for evolving systems based on dynamical systems theory; (3) analyse the evolving behaviour of various systems by using the formal model so far developed. First of all, it is argued that a system, which can be recognized by an observer as a system, is characterised by some emergent properties at a certain level of discourse. These properties are the results of the interactions between the system as components but not reducible to the individual or summative properties of those components. Any system is such an emergent and organized whole, and this whole can be defined and described as an emergent attractor. To maintain the wholeness in a changing environment, an open system may undergo radical changes both in its structure and function. The process of change is what is called of systems evolution. On reviewing the existing theories of self-organization, such as "Theory of Dissipative Structure", "Synergetics", "Hypercycle", "Cellular Automata", "Random Boolean Network" et al., a general conceptual framework for systems evolution has been outlined and it is based on the concept of emergent attractor for open systems. The emphasis is placed on the structural aspect of the process of change. Modem mathematical dynamical systems theory, with the study of nonlinear dynamics as its core, can provide (a) the concept of "attractor" to describe a system as an organized whole; (b) simple geometrical models of complex behaviour, (c) a complete taxonomy of attractors and bifurcation patterns; (d) a mathematical rationale for the explanations of evolutionary processes. Based on this belief, a formal model of evolving systems has been developed by using the language of mathematical dynamical systems theory (DST). Attractors and emergent attractors are formally defined. It is argued that the state of any systems can be described by one of the four fundamental types of attractors ( i. e. point attractor, periodic attractor, quasiperiodic attractor, chaotic attractor) at a certain level. The evolving behaviour of open systems can be analyzed by looking at the loss of structural stability in the systems. For a full analysis of systems evolution, the emphasis is put on the nonlinear inner dynamics which governs evolving systems. In trying to apply this conceptual framework and formal model, the evolving behaviour of various systems at different levels have been discussed. Among them are Benard cells in hydrodynamics, Brusselator in chemical systems, replicator systems in biology (hypercycle), predator-prey-food systems in ecology, and artificial neural networks. The complex dynamical behaviour of these systems, like the existence of various types of attractors and the occurrences of bifurcation when the environment changes, have been discussed. In most of the examples, the results in previous studies are cited directly and they are only re-interpreted by using the conceptual framework and the formal model developed in this research. In the study of artificial neural networks, a simple cellular automata network with only three neurons has been constructed and the activation dynamics has been analysed according to the formal model. Different attractors representing different dynamical behaviour of this network have been identified (point, periodic, quasiperiodic, and chaotic attractor). Similar discussions have been applied to a coupled Wilson-Cowan net. It is believed that the study of systems evolution is one of those attempts to bring systems science out of its primitive stage in which it ought not to be

Cellular Automata

Modelling and simulation are disciplines of major importance for science and engineering. There is no science without models, and simulation has nowadays become a very useful tool, sometimes unavoidable, for development of both science and engineering. The main attractive feature of cellular automata is that, in spite of their conceptual simplicity which allows an easiness of implementation for computer simulation, as a detailed and complete mathematical analysis in principle, they are able to exhibit a wide variety of amazingly complex behaviour. This feature of cellular automata has attracted the researchers' attention from a wide variety of divergent fields of the exact disciplines of science and engineering, but also of the social sciences, and sometimes beyond. The collective complex behaviour of numerous systems, which emerge from the interaction of a multitude of simple individuals, is being conveniently modelled and simulated with cellular automata for very different purposes. In this book, a number of innovative applications of cellular automata models in the fields of Quantum Computing, Materials Science, Cryptography and Coding, and Robotics and Image Processing are presented