Related papers: Discrete Dynamical Systems with Random Impulses
We introduce a family of discrete dynamical systems which includes, and generalizes, the mutation dynamics of rank two cluster algebras. These systems exhibit behavior associated with integrability, namely preservation of a symplectic form,…
To study discrete dynamical systems of different types --- deterministic, statistical and quantum --- we develop various approaches. We introduce the concept of a system of discrete relations on an abstract simplicial complex and develop…
Starting from kicked equations of motion with derivatives of non-integer orders, we obtain "fractional" discrete maps. These maps are generalizations of well-known universal, standard, dissipative, kicked damped rotator maps. The main…
In this paper, we introduce the notion of distributional chaos and the measure of chaos for random dynamical systems generated by two interval maps. We give some sufficient conditions for a zero measure of chaos and examples of chaotic…
Stability and bifurcation properties of one-dimensional discrete dynamical systems with positivity, which are derived from continuous ones by tropical discretization, are studied. The discretized time interval is introduced as a bifurcation…
We study invariant sets and measures generated by iterated function systems defined on countable discrete spaces that are uniform grids of a finite dimension. The discrete spaces of this type can be considered as models of spaces in which…
Dynamical behaviour of discrete dynamical systems has been investigated extensively in the past few decades. However, in several applications, long term memory plays an important role in the evolution of dynamical variables. The definition…
In this paper, we investigate the dynamics on the hyperspace induced by a non-autonomous dynamical system $(X,\mathbb{F})$, where the non-autonomous system is generated by a sequence $(f_n)$ of continuous self maps on $X$. We relate the…
The articulation process of dynamical networks is studied with a functional map, a minimal model for the dynamic change of relationships through iteration. The model is a dynamical system of a function $f$, not of variables, having a…
Propulsion of otherwise passive objects is achieved by mechanisms of active driving. We concentrate on cases in which the direction of active drive is subject to spontaneous symmetry breaking. In our case, this direction will be maintained,…
This paper presents a theoretical study on the influence of a discrete element in the nonlinear dynamics of a continuous mechanical system subject to randomness in the model parameters. This system is composed by an elastic bar, attached to…
We introduce simple models of genetic regulatory networks and we proceed to the mathematical analysis of their dynamics. The models are discrete time dynamical systems generated by piecewise affine contracting mappings whose variables…
A multidimensional chaos is generated by a special initial value problem for the non-autonomous impulsive differential equation. The existence of a chaotic attractor is shown, where density of periodic solutions, sensitivity of solutions…
Some properties of random Conley index are obtained and then a sufficient condition for the existence of abstract bifurcation points for both discrete-time and continuous-time random dynamical systems is presented. This stochastic…
We introduce a two-dimensional discrete-time dynamical system which represents the evolution of an angle and angular velocity. While the angle evolves by a fixed amount in every step, the evolution of the angular velocity is governed by a…
We discuss recent work on the static and dynamical properties of the asymmetric exclusion process, generalized to include the effect of disorder. We study in turn: random disorder in the properties of particles; disorder in the spatial…
We investigate the stability properties of discrete and hybrid stochastic nonlinear dynamical systems. More precisely, we extend the stochastic contraction theorems (which were formulated for continuous systems) to the case of discrete and…
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…
We aim at an understanding of the dynamical properties of a periodically driven damped harmonic oscillator coupled to a Random Field Ising Model (RFIM) at zero temperature, which is capable to show complex hysteresis. The system is a…
Let $(X,d)$ be a compact metric space and $f:X \to X$ be a self-map. The compact dynamical system $(X,f)$ is called sensitive or sensitivity depends on initial conditions, if there is a positive constant $\delta$ such that in each non-empty…