Related papers: Complex Systems with Trivial Dynamics
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple…
The classical Lorenz lowest order system of three nonlinear ordinary differential equations, capable of producing chaotic solutions, has been generalized by various authors in two main directions: (i) for number of equations larger than…
Modelling the dynamics of dense granular media is a long standing challenge and essential to many natural phenomena and technological applications. Here, we trace back puzzling experimental observation of detailed-balanced steady states to…
Let $(X,G)$ be a minimal equicontinuous dynamical system, where $X$ is a compact metric space and $G$ some topological group acting on $X$. Under very mild assumptions, we show that the class of regular almost automorphic extensions of…
The modeling of complex systems such as ecological or socio-economic systems can be very challenging. Although various modeling approaches exist, they are generally not compatible and mutually consistent, and empirical data often do not…
We propose a simple model that describes the dynamics of efficiencies of competing agents. Agents communicate leading to increase of efficiencies of underachievers, and an efficiency of each agent can increase or decrease irrespectively of…
We present a minimal agent-based model of interacting agents characterized by their wealth to study taxation and inequality in a non-conservative economy. Wealth evolves through an extremal stochastic replacement process in which the…
We relate progress in statistical mechanics, both at and far from equilibrium, to advances in the theory of dynamical systems. We consider computer simulations of time-reversible deterministic chaos in small systems with three- and…
We consider a class of cubic stochastic operators that are motivated by models for evolution of frequencies of genetic types in populations. We take populations with three mutually exclusive genetic types. The long term dynamics of single…
Dissipative phenomena manifest in multiple mechanical systems. In this dissertation, different geometric frameworks for modelling non-conservative dynamics are considered. The objective is to generalize several results from conservative…
We present and analyze a model for the evolution of the wealth distribution within a heterogeneous economic environment. The model considers a system of rational agents interacting in a game theoretical framework, through fairly general…
Consistent statistical physical description is given for systems where the elementary excitations are composite objects. Explicit calculational scheme is constructed for the energy density and the total number of thermodynamical degrees of…
In this paper, we consider a simple kinetic model of economy involving both exchanges between agents and speculative trading. We show that the kinetic model admits non trivial quasi-stationary states with power law tails of Pareto type. In…
We show that an equilibriumlike additivity property can remarkably lead to power-law distributions observed frequently in a wide class of out-of-equilibrium systems. The additivity property can determine the full scaling form of the…
Multifield models with a curved field space have already been shown to be able to provide viable quintessence models for steep potentials that satisfy swampland bounds. The simplest dynamical systems of this type are obtained by coupling…
Consider briefly the equations of fluid dynamics-they describe the enormous wealth of detail in all the interacting physical elements of a fluid flow-whereas in applications we want to deal with a description of just that which is…
An algebraic characterization of the property of approximate controllability is given, for behaviours of spatially invariant dynamical systems, consisting of distributional solutions, that are periodic in the spatial variables, to a system…
Symmetries play a conspicuous role in the large-scale behavior of critical systems. While in equilibrium they allow to classify asymptotics into different universality classes, out of equilibrium they can emerge, some times unexpectedly, as…
We give sufficient conditions for asymptotic stabilization of equilibrium points and periodic orbits of a dynamical system when we add a geometric dissipation of gradient type. We also describe the domain of attraction in the case of…
A large variety of interacting complex systems are characterized by interactions occurring between more than two nodes. These systems are described by simplicial complexes. Simplicial complexes are formed by simplices (nodes, links,…