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In this article, we present a brief overview of some of the recent progress made in identifying and generating finite dimensional integrable nonlinear dynamical systems, exhibiting interesting oscillatory and other solution properties,…
The long-time evolution of a system in interaction with an external environment is usually described by a family of linear maps g_t, generated by master equations of Block-Redfield type. These maps are in general non-positive; a widely…
We have performed the dynamical system analysis to obtain the critical point in which, the value of the geometric and dynamical parameters satisfy the late-time cosmic behavior of the Universe. At the outset, the modified Friedmann…
Nonequilibrium steady states in driven diffusive systems exhibit many features which are surprising or counterintuitive, given our experience with equilibrium systems. We introduce the prototype model and review its unusual behavior in…
The vast majority of the literature dealing with quantum dynamics is concerned with linear evolution of the wave function or the density matrix. A complete dynamical description requires a full understanding of the evolution of measured…
We study discrete dynamical systems through the topological concepts of limit set, which consists of all points that can be reached arbitrarily late, and asymptotic set, which consists of all adhering values of orbits. In particular, we…
We investigate the cosmological behavior of mimetic F(R) gravity. This scenario is the F(R) extension of usual mimetic gravity classes, which are based on re-parametrizations of the metric using new, but not propagating, degrees of freedom,…
The motion of a spinning football brings forth the possible existence of a whole class of finite dynamical systems where there may be non-denumerably infinite number of fixed points. They defy the very traditional meaning of the fixed point…
A nonautonomous dynamical system $(\boldsymbol{X},\boldsymbol{T})=\{(X_{k},T_{k})\}_{k=0}^{\infty}$ is a sequence of continuous mappings $T_{k}:X_{k} \to X_{k+1}$ along with a sequence of compact metric spaces $X_{k}$. In this paper, we…
A detailed discussion of the coherent and incoherent dynamic structure function of the free Fermi gas at finite temperature is presented. Their behavior and evolution with the momentum transfer and the temperature is analyzed, while…
We argue that simple dynamical systems are factors of finite automata, regarded as dynamical systems on discontinuum. We show that any homeomorphism of the real interval is of this class. An orientation preserving homeomorphism of the…
A finite dynamical system with $n$ components is a function $f:X\to X$ where $X=X_1\times\dots\times X_n$ is a product of $n$ finite intervals of integers. The structure of such a system $f$ is represented by a signed digraph $G$, called…
Flow networks can describe many natural and artificial systems. We present a model for a flow system that allows for volume accumulation, includes conduits with a non-linear relation between current and pressure difference, and can be…
A simple weakly frequency dependent model for the dynamics of a population with a finite number of types is proposed, based upon an advantage of being rare. In the infinite population limit, this model gives rise to a non-smooth dynamical…
We study long-range interacting systems driven by external stochastic forces that act collectively on all the particles constituting the system. Such a scenario is frequently encountered in the context of plasmas, self-gravitating systems,…
In this manuscript, we investigate a fractional stochastic neutral differential equation with time delay, which includes both deterministic and stochastic components. Our primary objective is to rigorously prove the existence of a unique…
We investigate explicit functions that can produce truly random numbers. We use the analytical properties of the explicit functions to show that certain class of autonomous dynamical systems can generate random dynamics. This dynamics…
Two cases of a phenomenological model for ferromagnetism are considered, discrete and continuous. And the relationship, in general, between discrete and continuous models explored. In a similar way to the logistic map behavior, the…
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…
In this paper, we study the dynamical properties of actions on the space of compact subsets of the phase space. More precisely, if $X$ is a metric space, let $2^X$ denote the space of non-empty compact subsets of $X$ provided with the…