Related papers: Chaos in Saw Map
In this article, we attempt to study the possible link between the dynamics of a circle map and the caustics of its iterations. The attention is on a geometrically defined off-center reflections, which, coincidentally, is also a…
Chaotic systems which are due to nonlinearity have attracted a great concern in the current world and chaotic models. Systems for a wide range of operation conditions have their application in almost all branches of engineering and science.…
We study the dynamics of a piecewise map defined on the set of three pairwise nonparallel, nonconcurrent lines in $\mathbb{R}^2$. The geometric map of study may be analogized to the billiard map with a different reflection rule so that each…
In recent years, the topic of car-following has experimented an increased importance in traffic engineering and safety research. This has become a very interesting topic because of the development of driverless cars…
The efficient detection of chaotic behavior in orbits of a complex dynamical system is an active domain of research. Several indicators have been proposed in the past, and new ones have recently been developed in view of improving the…
We analyze the dynamics of a deterministic model of inhibitory neuronal networks proving that the discontinuities of the Poincare map produce a never empty chaotic set, while its continuity pieces produce stable orbits. We classify the…
Dynamical systems on the interval were widely studied because they are among the simplest systems and nevertheless they turn out to have complex dynamics. Many works on chaos were inspired by the behaviour of interval maps. However these…
Experimental records of active bundle motility are used to demonstrate the presence of a low-dimensional chaotic attractor in hair cell dynamics. Dimensionality tests from dynamic systems theory are applied to estimate the number of…
Chaos is popularly associated with its property of sensitivity to initial conditions. In this paper we will show that there can be a flip side to this property which is quite fascinating and highly useful in many applications. As a result,…
We introduce a model of Poincar\'e mappings which represents hierarchical structure of phase spaces for systems with many degrees of freedom. The model yields residence time distribution of power type, hence temporal correlation remains…
We discuss Devaney chaos on compact metric spaces using a decomposition space characterized by topological nature of symbolic dynamics. A chaotic map obtained here is defined as a topologically conjugate of the chaotic map on a…
Hierarchy of one-parameter families of chaotic maps with an invariant measure have been introduced, where their appropriate coupling has lead to the generation of some coupled chaotic maps with an invariant measure. It is shown that these…
We here show that the family of finite-dimensional, discrete-time, passive, linear time-invariant systems can be characterized through the structure of maximal, matrix-convex set, closed under multiplication among its elements. Moreover,…
Non-linear dynamics is not a usually covered topic in undergraduate physics courses. However, its importance within classical mechanics and the general theory of dynamical systems is unquestionable. In this work we show that this subject…
We study two-dimensional, two-piece, piecewise-linear maps having two saddle fixed points. Such maps reduce to a four-parameter family and are well known to have a chaotic attractor throughout open regions of parameter space. The purpose of…
For a class of quantized open chaotic systems satisfying a natural dynamical assumption, we show that the study of the resolvent, and hence of scattering and resonances, can be reduced to the study of a family of open quantum maps, that is…
We visit a previously proposed discontinuous, two-parameter generalization of the continuous, one-parameter logistic map and present exhaustive numerical studies of the behavior for different values of the two parameters and initial points.…
We develop the characterization of the dynamics at the noise-perturbed edge of chaos in logistic maps in terms of the quantities normally used to describe glassy properties in structural glass formers. Following the recognition [Phys. Lett.…
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…
Despite many of the most common chaotic dynamical systems being continuous in time, it is through discrete time mappings that much of the understanding of chaos is formed. Henri Poincar\'e first made this connection by tracking consecutive…