Related papers: What can one learn about Self-Organized Criticalit…
We study the noisy dynamics of a close relative of the sand pile model. Depending on the type of noise and the time scale of observation, we find stationary fluctuations (similar to SOC) or an aging dynamics with punctuated equilibria, a…
Consider the convex hull of a collection of disjoint open discs with radii $1/2$. The boundary of the convex hull consists of a finite number of line segments and arcs. Randomly choose a point in one of the arcs in the boundary so that the…
A succesful method to describe the asymptotic behavior of a discrete time stochastic process governed by some recursive formula is to relate it to the limit sets of a well chosen mean differential equation. Under an attainability condition,…
In this article, one defines two models of adaptive systems: the meta-dynamical adaptive system using the notion of Kalman dynamical systems and the adaptive differential equations using the notion of variable dimension spaces. This concept…
Within a mathematical model, the metabolic process of glycolysis is studied. The general scheme of glycolysis is considered as a natural result of the biochemical evolution. By using the theory of dissipative structures, the conditions of…
The mechanism of self-organized criticality is based on a steady slow loading and a quick huge stress-release. We add the clustering of the events in space and time to the Bak-Tang-Wiesenfeld cellular automaton and obtain the truncated…
The Stock Market is a complex self-interacting system, characterized by an intermittent behaviour. Periods of high activity alternate with periods of relative calm. In the present work we investigate empirically about the possibility that…
We introduce a model for self-organized dynamics which, we argue, addresses several drawbacks of the celebrated Cucker-Smale (C-S) model. The proposed model does not only take into account the distance between agents, but instead, the…
A fractal is in essence a hierarchy with cascade structure, which can be described with a set of exponential functions. From these exponential functions, a set of power laws indicative of scaling can be derived. Hierarchy structure and…
The modification of the model of P.Bak and K.Sneppen of the self-organized biological evolution is proposed on the basis of a formalization of the scheme of the biosphere evolution suggested by O.V.Kovalev. This scheme is regarded as one…
Cyclicity and instability inherent in the economy can manifest themselves in irregular fluctuations, including chaotic ones, which significantly reduces the accuracy of forecasting the dynamics of the economic system in the long run. We…
We study a directed coupled map lattice model in two dimensions, with two degrees of freedom associated with each lattice site. The two freedoms are coupled at a fraction $c$ of lattice bonds acting as quenched random defects. In the case…
Continuous cellular automata (CCAs) have evolved from discrete lookup tables to continuous partial differential equation (PDE) formulations in the search for novel forms of complexity. Despite innovations in qualitative behavior, analytical…
For linear dynamical systems (in continuous-time and discrete-time) we revisit and extend the concepts of hypocoercivity and hypocontractivity and give a detailed analysis of the relations of these concepts to (asymptotic) stability, as…
We investigate, by numerical simulations, how the avalanche dynamics of the Bak-Tang-Wiesenfeld (BTW) sandpile model can induce emergence of scale-free (SF) networks and how this emerging structure affects dynamics of the system. We also…
Dipolar fluids are known to exhibit complex self-assembly at low temperatures, yet a compact thermodynamic description of their aggregate statistics has remained elusive. Using molecular dynamics simulations of Stockmayer particles with a…
In this paper we study the diffusely observed occurrence of Fractality and Self-organized Criticality in mechanical systems. We analytically show, based on a prototypical compressed tensegrity structure, that these phenomena can be viewed…
In this article we develop a general technique which takes a known characterization of a property for weighted backward shifts and lifts it up to a characterization of that property for a large class of operators on $L^p(X)$. We call these…
Many theories of physical interest, which admit a Hamiltonian description, exhibit symmetries under a particular class of non - strictly canonical transformation, known as dynamical similarities. The presence of such symmetries allows a…
We consider the concept of statistical complexity to write the quasiperiodical damped systems applying the snapshot attractors. This allows us to understand the behaviour of these dynamical systems by the probability distribution of the…