Complex systems present problems both in mathematical modelling and philosophical foundations. The study of complex systems represents a new approach to science that investigates how relationships between parts give rise to the collective behaviors of a system and how the system interacts and forms relationships with its environment. The equations from which models of complex systems are developed generally derive from statistical physics, information theory and non-linear dynamics, and represent organized but unpredictable behaviors of natural systems that are considered fundamentally complex.
World food supply is crucial to the well-being of every human on the planet in the basic sense that we need food to live. It also has a profound impact on the world economy, international trade and global political stability.Furthermore, consumption of certain types and amounts foods can affect health,and the choice of livestock and plants for food production can impact sustainable use of global resources. There are communities where insufficient food causes nutritional deficiencies, and at the same time other communities eating too much food leading to obesity and accompanying diseases. These aspects reflect the utmost importance of agricultural production and conversion of commodities to food products. Moreover, all factors contributing to the food supply are interdependent, and they are an integrative part of the continuously changing, adaptive and interdependent systems in the world around us. The properties of such interdependent systems usually cannot be inferred from the properties of its parts. In addressing current challenges, like the apparent incongruences of obesity and hunger, we have to account for the complex interdependencies among areas such as physics and sociology. This is possible using the complex system approach. It encompasses an integrative multi-scale and inter-disciplinary approach. Using a complex system approach that accounts for the needs of stakeholders in the agriculture and food domain, and determines which research programs will enable these stakeholders to better anticipate emerging developments in the world around them, will enable them to determine effective intervention strategies to simultaneously optimise and safeguard their interests and the interests of the environment.
If the evolving variable is two- or three-dimensional, the attractor of the dynamic process can be represented geometrically in two or three dimensions, (as for example in the three-dimensional case depicted to the right). An attractor can be a point, a finite set of points, a curve, a manifold, or even a complicated set with a fractal structure known as a strange attractor. If the variable is a scalar, the attractor is a subset of the real number line. Describing the attractors of chaotic dynamical systems has been one of the achievements of chaos theory.
A trajectory of the dynamical system in the attractor does not have to satisfy any special constraints except for remaining on the attractor. The trajectory may be periodic or chaotic. If a set of points is periodic or chaotic, but the flow in the neighbourhood is away from the set, the set is not an attractor, but instead is called a repeller (or repellor).
In a combinatorial communication system, some signals consist of the combinations of other signals. Such systems are more efficient than equivalent, non-combinatorial systems, yet despite this they are rare in nature. Why? Previous explanations have focused on the adaptive limits of combinatorial communication, or on its purported cognitive difficulties, but neither of these explains the full distribution of combinatorial communication in the natural world. Here we present a nonlinear dynamical model of the emergence of combinatorial communication that, unlike previous models, considers how initially non-communicative behaviour evolves to take on a communicative function. We derive three basic principles about the emergence of combinatorial communication. We hence show that the interdependence of signals and responses places significant constraints on the historical pathways by which combinatorial signals might emerge, to the extent that anything other than the most simple form of combinatorial communication is extremely unlikely. We also argue that these constraints can be bypassed if individuals have the socio-cognitive capacity to engage in ostensive communication. Humans, but probably no other species, have this ability. This may explain why language, which is massively combinatorial, is such an extreme exception to nature's general trend for non-combinatorial communication.
Edgar Morin 5.0 out of 5 stars 6 Star Foundation Work for Everything Else, August 19, 2013 This is a remarkably coherent book about the most important topic for all of us, the matter of complexity and more to the point, thinking about complexity.
The Interdisciplinary Center for Nonlinear Phenomena and Complex Systems comprises scientists holding permanent positions with the Université libre de Bruxelles (ULB) and the Belgian Fund for Scientific Research (FNRS), post-doctoral fellows and doctoral students. It is an interdisciplinary research center gathering laboratories from the departments of Physics, Chemistry and Biology of the Faculty of Sciences, the Faculty of Applied Sciences, and the Faculty of Medecine of the ULB. Each year several visitors are hosted for periods ranging from a few days to several months.
The Center is dedicated to promoting the science of nonlinear phenomena and complex systems, by conducting research and training in this interdisciplinary area, by participating in national and international collaborations, and by organizing workshops and advanced courses. Its main expertise is in thermodynamics, statistical mechanics, nonlinear dynamics and chaos theory, stochastic processes, quantum physics, physical chemistry as well as simulation techniques. The tools developed in this framework are applied to the study of complex systems, from chemical kinetics, fluid mechanics and materials science to biology.
The Complex Systems and Networks Lab (COSNET) is part of the Institute for Biocomputation and Physics of Complex Systems (BIFI) of the University of Zaragoza, and is mainly devoted to investigate the laws governing the structure and dynamics of complex networked systems.
Cybernetics and Systems Research (CSR) were developed in the mid-twentieth century, offering the possibility of describing and comparing different phenomena using the same language. The concepts which originated in CSR have spread to practically all disciplines, many now used within the scientific study of complex systems. CSR has the potential to contribute to the solution of relevant problems, but the path towards this goal is not straightforward. This paper summarizes the ideas presented by the authors during a round table in 2012 on the past, present and future of CSR.
There is mounting evidence of the apparent ubiquity of scale-free networks among complex systems. Many natural and physical systems exhibit patterns of interconnection that conform, approximately, to the structure expected of a scale-free network. We propose an efficient algorithm to generate representative samples from the space of all networks defined by a particular(scale-free) degree distribution. Using this algorithm we are able to systematically explore that space with some surprising results: in particular,we find that preferential attachment growth models do not yield typical realizations and that there is a certain latent structure among such networks--- which we loosely term "hub-centric". We provide a method to generate or remove this latent hub-centric bias --- thereby demonstrating exactly which features of preferential attachment networks are atypical of the broader class of scale free networks. Based on these results we are also able to statistically determine whether experimentally observed networks are really typical realizations of a given degree distribution (scale-free degree beingthe example which we explore). In so doing we propose a surrogate generation method for complex networks, exactly analogous the the widely used surrogate tests of nonlinear time series analysis.
Fritjof Capra, in his book ‘The Hidden Connections’ applies aspects of complexity theory, particularly the analysis of networks, to global capitalism and the state of the world; and eloquently argues the case that social systems such as organisations and networks are not just like living systems – they are living systems. The concept and theory of living systems (technically known as autopoiesis) was introduced in 1972 by Chilean biologists Humberto Maturana and Francisco Varela.
This is a complete version of a ‘long-blog’ written by Al Kennedy on behalf of ‘The Nature of Business’ blog and BCI: Biomimicry for Creative Innovation www.businessinspired...
At TED2010, mathematics legend Benoit Mandelbrot develops a theme he first discussed at TED in 1984 -- the extreme complexity of roughness, and the way that fractal math can find order within patterns that seem unknowably complicated.
The PyCX Project aims to develop an online repository of simple, crude, yet easy-to-understand Python sample codes for dynamic complex systems simulations, including iterative maps, cellular automata, dynamical networks and agent-based models.
The International Research Center for Mathematics & Mechanics of Complex Systems (M&MoCS) is a Research Center of the Università dell’Aquila. It was established by the Dipartimento di Ingegneria delle Strutture, delle Acque e del Terreno (DISAT) and the Dipartimento di Matematica Pura e Applicata (DMPA).
Its administrative headquarters are located in L’Aquila and its scientific center is in Cisterna di Latina. M&MoCS was established with the financial and logistical support of Provincia di Latina and the Fondazione Tullio Levi-Civita, with which it shares the mission of developing and disseminating scientific culture in the region. It was also founded together with the Dipartimento di Strutture of Università di Roma Tre.