Related papers: A-coupled-expanding and distributional chaos
We prove that the set of maps which exhibit distributional chaos of type 1 (DC1) is $C^0$-dense in the space of continuous self-maps of given any compact topological manifold (possibly with boundary).
The bifurcation and chaotic behaviour of unidirectionally coupled deterministic ratchets is studied as a function of the driving force amplitude ($a$) and frequency ($\omega$). A classification of the various types of bifurcations likely to…
This paper formulates a new approach to the study of chaos in discrete dynamical systems based on the notions of inverse ill-posed problems, set-valued mappings, generalized and multivalued inverses, graphical convergence of a net of…
Cycling chaos is a heteroclinic connection between several chaotic attractors, at which switching between the chaotic sets occur at growing time intervals. Here we characterize the coherence properties of these switchings, considering…
The dynamics of one dimensional iterative maps in the regime of fully developed chaos is studied in detail. Motivated by the observation of dynamical structures around the unstable fixed point we introduce the geometrical concept of a…
A new approach to clustering, based on the physical properties of inhomogeneous coupled chaotic maps, is presented. A chaotic map is assigned to each data-point and short range couplings are introduced. The stationary regime of the system…
The scope of this teaching package is to make a brief introduction to some notions and properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using…
The appearance of infinitely-many period-doubling cascades is one of the most prominent features observed in the study of maps depending on a parameter. They are associated with chaotic behavior, since bifurcation diagrams of a map with a…
A compound tunneling mechanism from one integrable region to another mediated by a delocalized state in an intermediate chaotic region of phase space was recently introduced to explain peculiar features of tunneling in certain…
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,…
By choosing a dynamical system with d different couplings, one can rearrange a system based on the graph with given vertex dependent on the dynamical system elements. The relation between the dynamical elements (coupling) is replaced by a…
We predict that continuously monitored quantum dynamics can be chaotic. The optimal paths between past and future boundary conditions can diverge exponentially in time when there is time-dependent evolution and continuous weak monitoring.…
A model with hyperchaos is studied by means of Lyapunov two-parameter analysis. The regions of chaos and hyperchaos, as well as autonomous quasiperiodicity are identified. We discuss the picture of domains of different regimes in the…
Characterizing the emergence of chaotic dynamics of complex networks is an essential task in nonlinear science with potential important applications in many fields such as neural control engineering, microgrid technologies, and ecological…
We investigate the spatio-temporal dynamics of coupled chaotic systems with nonlocal interactions, where each element is coupled to its nearest neighbors within a finite range. Depending upon the coupling strength and coupling radius, we…
We present a new chaotic system of three coupled ordinary differential equations, limited to quadratic nonlinear terms. A wide variety of dynamical regimes are reported. For some parameters, chaotic reversals of the amplitudes are produced…
Hypersensitivity to perturbation is a criterion for chaos based on the question of how much information about a perturbing environment is needed to keep the entropy of a Hamiltonian system from increasing. We demonstrate numerically that…
The collective behavior of a coupled map lattice having {\it unbounded} chaotic local dynamics is investigated through the properties of its mean field. The presence of unstable periodic orbits in the local maps determines the emergence of…
Deterministic chaos is phenomenon from nonlinear dynamics and it belongs to greatest advances of twentieth-century science. Chaotic behavior appears apart of mathematical equations also in wide range in observable nature, so as in there…
One of the common characteristics of chaotic maps or flows in high dimensions is "unstable dimensional variability", in which there are periodic points whose unstable manifolds have different dimensions. In this paper, in trying to…