Related papers: Chaos in Saw Map
A qualitative and quantitative extension of the chaotic models used to generate self-similar traffic with long-range dependence (LRD) is presented by means of the formulation of a model that considers the use of piecewise affine…
This paper studies how complicated and irregular behavior, known as chaos, can arise in a simple mathematical model that includes time delays. The model is a delay differential equation in which the present rate of change depends not only…
We study a deterministic dynamics with two time scales in a continuous state attractor network. To the usual (fast) relaxation dynamics towards point attractors (``patterns'') we add a slow coupling dynamics that makes the visited patterns…
We present a method based on symbolic dynamics for the detection of synchronization in networks of coupled maps and distinguishing between chaotic and random iterations. The symbolic dynamics are defined using special partitions of the…
With the constant increase of the number of autonomous vehicles and connected objects, tools to understand and reproduce their mobility models are required. We focus on chaotic dynamics and review their applications in the design of…
A discrete dynamical system in Euclidean m-space generated by the iterates of an asymptotically zero map f, satisfying f(x) goes to zero as x goes to infinity, must have a compact global attracting set $A $. The question of what additional…
Topologically chaotic fluid advection is examined in two-dimensional flows with either or both directions spatially periodic. Topological chaos is created by driving flow with moving stirrers whose trajectories are chosen to form various…
Control laws for continuous-time dynamical systems are most often implemented via digital controllers using a sample-and-hold technique. Numerical discretization of the continuous system is an integral part of subsequent analysis. Feedback…
The paper deals with the theoretical analysis of a logistic system composed of at least two elements with distributed parameters. It has been shown that such a system may generate specific oscillations in spite of the fact that the…
Effect of noise in inducing order on various chaotically evolving systems is reviewed, with special emphasis on systems consisting of coupled chaotic elements. In many situations it is observed that the uncoupled elements when driven by…
The phase ordering properties of lattices of band-chaotic maps coupled diffusively with some coupling strength $g$ are studied in order to determine the limit value $g_e$ beyond which multistability disappears and non-trivial collective…
A novel type of self-organized lattice in which chaotic defects are arranged periodically is reported for a coupled map model of open flow. We find that temporally chaotic defects are followed by spatial relaxation to an almost periodic…
A model of interacting motile chaotic elements is proposed. The chaotic elements are distributed in space and interact with each other through interactions depending on their positions and their internal states. As the value of a governing…
We prove the holding of chaos in the sense of Li-Yorke for a family of four-dimensional discrete dynamical systems that are naturally associated to ODE systems describing coupled oscillators subject to an external non-conservative force,…
In this paper we consider a family of system with 2 predators feeding on one prey. We show how to construct a positively invariant set in which it is possible to define a Poincar\'e map for examining the behaviour of the system, mainly in…
The advection and diffusion of a passive scalar is investigated for a map of the 2-torus. The map is chaotic, and the limit of almost-uniform stretching is considered. This allows an analytic understanding of the transition from a phase of…
We investigate species-rich mathematical models of ecosystems. While much of the existing literature focuses on the properties of equilibrium fixed points, persistent dynamics (e.g., limit cycles or chaos) have also been observed, both in…
Two-dimensional mappings obtained by coupling two piecewise increasing expanding maps are considered. Their dynamics is described when the coupling parameter increases in the expanding domain. By introducing a coding and by analysing an…
We consider a dissipative version of the standard nontwist map. Nontwist systems present a robust transport barrier, called the shearless curve, that becomes the shearless attractor when dissipation is introduced. This attractor can be…
The dynamics of an extended, spatiotemporally chaotic system might appear extremely complex. Nevertheless, the local dynamics, observed through a finite spatiotemporal window, can often be thought of as a visitation sequence of a finite…