Related papers: Dynamical systems as enriched functors
The well-defined but intricate course of time evolution exhibited by many naturally occurring phenomena suggests some source of dynamic order sustaining it. In spite of its obviousness as a problem, it has remained absent from the…
We consider a specific dynamical system of groups formation. It is based simultaneously on a gradient competition between groups and a strong accumulation inside groups. Such a dynamical system demonstrates interesting behavior of densities…
We introduce index systems, a tool for studying isolated invariant sets of dynamical systems that are not necessarily hyperbolic. The mapping of the index systems mimics the expansion and contraction of hyperbolic maps on the tangent space,…
The asynchronous systems are the non-deterministic models of the asynchronous circuits from the digital electrical engineering. In the autonomous version, such a system is a set of functions x:R{\to}{0,1}^{n} called states (R is the time…
In dynamical systems composed of interacting parts, conditional exponents, conditional exponent entropies and cylindrical entropies are shown to be well defined ergodic invariants which characterize the dynamical selforganization and…
Motions carry information about the underlying task being executed. Previous work in human motion analysis suggests that complex motions may result from the composition of fundamental submovements called movemes. The existence of finite…
The thermodynamic formalism allows one to access the chaotic properties of equilibrium and out-of-equilibrium systems, by deriving those from a dynamical partition function. The definition that has been given for this partition function…
Dynamical symmetries are of considerable importance in elucidating the complex behaviour of strongly interacting systems with many degrees of freedom. Paradigmatic examples are cooperative phenomena as they arise in phase transitions, where…
The automorphism group of a one dimensional shift space over a finite alphabet exhibits different types of behavior: for a large class with positive entropy, it contains a rich collection of subgroups, while for many shifts of zero entropy,…
Component substitution has numerous practical applications and constitutes an active research topic. This paper proposes to enrich an existing component-based framework--a model with dynamic reconfigurations making the system evolve--with a…
We present the first steps of interaction spaces theory, a universal mathematical theory of complex systems which is able to embed cellular automata, agent based models, master equation based models, stochastic or deterministic, continuous…
There are two main approaches to non-equlibrium statistical mechanics: one using stochastic processes and the other using dynamical systems. To model the dynamics during inflation one usually adopts a stochastic description, which is known…
In describing a dynamical system, the greatest part of the work for a theoretician is to translate experimental data into differential equations. It is desirable for such differential equations to admit a Lagrangian and/or an Hamiltonian…
We develop a representation theory of categories as a means to explore characteristic structures in algebra. Characteristic structures play a critical role in isomorphism testing of groups and algebras, and their construction and…
It is well-known that biological phenomena are emergent. Emergent phenomena are quite interesting and amazing. However, they are difficult to be understood. Due to this difficulty, we propose a theory to describe emergence based on a…
Fields offer a versatile approach for describing complex systems composed of interacting and dynamic components. In particular, some of these dynamical and stochastic systems may exhibit goal-directed behaviors aimed at achieving specific…
One of the characteristic features of categorical systems theory is that the behavior of systems can be characterized by certain morphisms into them. In other words, behaviors form a representable covariant functor to Set. And more…
The quantum master equation is a widespread approach to describing open quantum system dynamics. In this approach, the effect of the environment on the system evolution is entirely captured by the dynamical generator, providing a compact…
A general dynamical system composed by two coupled sectors is considered. The initial time configuration of one of these sectors is described by a set of classical data while the other is described by standard quantum data. These dynamical…
The universal concept of complexity by the dynamic redundance paradigm and the ensuing concept of extended dynamic fractality (physics/9806002) are applied here to higher levels of complexity corresponding to living systems. After recalling…