Related papers: A mathematical definition of complex adaptive syst…
The concept of random dynamical system is a comparatively recent development combining ideas and methods from the well developed areas of probability theory and dynamical systems. Due to our inaccurate knowledge of the particular physical…
In order to apply thermodynamics to systems in which entropy is not extensive, it has become customary to define generalized entropies. While this approach has been effective, it is not the only possible approach. We suggest that some…
The paper proposes a general notion of interaction between attributes, which can be applied to many fields in decision making and data analysis. It generalizes the notion of interaction defined for criteria modelled by capacities, by…
Based on the probability distribution observed in complex systems and an assumption that the probability distributions of complex systems satisfy a new generalized multiplication, it is proved that the statistical theory of complex systems…
The sciences of complexity present some recurrent themes: the emergence of qualitatively new behaviors in dissipative systems out of equilibrium, the aparent tendency of complex system to lie at the border of phase transitions and…
This paper presents the foundational ideas for a new way of modeling social aggregation. Traditional approaches have been using network theory, and the theory of random networks. Under that paradigm, every social agent is represented by a…
Several approaches and corresponding definitions of complexity have been developed in different fields. Urban systems are the archetype of complex socio-technical systems concerned with these different viewpoints. We suggest in this chapter…
Many complex systems satisfy a set of constraints on their degrees of freedom, and at the same time, they are able to work and adapt to different conditions. Here, we describe the emergence of this ability in a simplified model in which the…
This paper considers systems subject to nonholonomic constraints which are not uniform on the whole configuration manifold. When the constraints change, the system undergoes a transition in order to comply with the new imposed conditions.…
In this paper, we develop a natural (empirical) relational theory for describing and modeling complex biological phenomena. We have as stepping stone the assertion: function implies structure. The theory is built upon a graph's theory…
We analyse the unreduced, nonperturbative dynamics of an arbitrary many-body interaction process with the help of the generalised effective potential method and reveal the well-specified universal origin of change (emergence), time and…
We present several philosophical ideas emerging from the studies of complex systems. We make a brief introduction to the basic concepts of complex systems, for then defining "abstraction levels". These are useful for representing…
This work introduces a general multi-level model for self-adaptive systems. A self-adaptive system is seen as composed by two levels: the lower level describing the actual behaviour of the system and the upper level accounting for the…
We argue that traditional Western science cannot adequately describe sports and other types of human behavior. Then we make an argument why a complex adaptive systems approach has the potential to provide the foundation for such a theory.…
Living systems, from single cells to higher vertebrates, receive a continuous stream of non-stationary inputs that they sense, e.g., via cell surface receptors or sensory organs. Integrating these time-varying, multi-sensory, and often…
After discussing the significance of interactions to understand complex multiscale stochastic systems (CMSS), we turn our attention to the construction of a Generalised Theory of Interactions (GToI). We define interactions as discrete,…
This paper proposes a systems approach to social sciences based on mathematical framework derived from a generalization of the mathematical kinetic theory and on theoretical tools of game theory. Social systems are modeled as a living…
We study analysis of complex systems using a Quantitative Theory of Meaning developed as an extention of Shannon's Communication Theory. The approach consideres complexity not in terms of the manifestation of its effects which are…
We revisit the behavioral approach to systems theory and make explicit the abstract pattern that governs it. Our end goal is to use that pattern to understand interaction-related phenomena that emerge when systems interact. Rather than…
Many branches of theoretical and applied mathematics require a quantifiable notion of complexity. One such circumstance is a topological dynamical system - which involves a continuous self-map on a metric space. There are many notions of…