Related papers: Patterns in the sine map bifurcation diagram
Area-preserving nontwist maps are used to describe a broad range of physical systems. In those systems, the violation of the twist condition leads to nontwist characteristic phenomena, such as reconnection-collision sequences and shearless…
For a continuous map on the unit interval or circle, we define the bifurcation set to be the collection of those interval holes whose surviving set is sensitive to arbitrarily small changes of their position. By assuming a global…
Symmetry reduction by the method of slices quotients the continuous symmetries of chaotic flows by replacing the original state space by a set of charts, each covering a neighborhood of a dynamically important class of solutions,…
The first step in investigating fractional difference maps, which do not have periodic points except fixed points, is to find asymptotically periodic points and bifurcation points and draw asymptotic bifurcation diagrams. Recently derived…
Bifurcation theory is the usual analytic approach to study the parameter space of a dynamical system. Despite the great power of prediction of these techniques, fundamental limitations appear during the study of a given problem. Nonlinear…
We review recent results that lead to a very precise understanding of the dynamics of typical unimodal maps from the statistical point of view. We also describe the (generalized) renormalization approach to the study of the statistical…
A procedure to characterize chaotic dynamical systems with concepts of complex networks is pursued, in which a dynamical system is mapped onto a network. The nodes represent the regions of space visited by the system, while edges represent…
We propose a new method for quantitative characterization of spatial network-like patterns with loops, such as surface fracture patterns, leaf vein networks and patterns of urban streets. Such patterns are not well characterized by purely…
Chaotic dynamics can be effectively studied by continuation from an anti-integrable limit. We use this limit to assign global symbols to orbits and use continuation from the limit to study their bifurcations. We find a bound on the…
The unitary evolution maps in closed chaotic quantum graphs are known to have universal spectral correlations, as predicted by random matrix theory. In chaotic graphs with absorption the quantum maps become non-unitary. We show that their…
We give piecewise affine maps on the unit cube whose symbolic representation is the Dyck shift. This leads to a different way of verifying the chaotic nature of this system, including the computation of entropy.
We consider chains of one-dimensional, piecewise linear, chaotic maps with uniform slope. We study the diffusive behaviour of an initially nonuniform distribution of points as a function of the slope of the map by solving Frobenius-Perron…
Large populations of globally-coupled identical maps subjected to independent additive noise are shown to undergo qualitative changes as the features of the stochastic process are varied. We show that for strong coupling, the collective…
We consider a family of singular maps as an example of a simple model of dynamical systems exhibiting the property of robust chaos on a well defined range of parameters. Critical boundaries separating the region of robust chaos from the…
Differentiable conjugacies link dynamical systems that share properties such as the stability multipliers of corresponding orbits. It provides a stronger classification than topological conjugacy, which only requires qualitative similarity.…
Chaos is an active research subject in the fields of science in recent years. it is a complex and an erratic behavior that is possible in very simple systems. in the present day, the chaotic behavior can be observed in experiments. Many…
Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear. Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However,…
Asymptotic state of an open quantum system can undergo qualitative changes upon small variation of system parameters. We demonstrate it that such 'quantum bifurcations' can be appropriately defined and made visible as changes in the…
We report a remarkable type of bifurcation: by varying real parameters, unstable complex orbits may become stable over wide parameter ranges. Thus, phase diagrams obtained by analizing solely the stability of real solutions may be…
At the intersection of two unidirectional traffic flows a stripe formation instability is known to occur. In this paper we consider coupled time evolution equations for the densities of the two flows in their intersection area. We show…