### A 3D Smale horseshoe in a hyperchaotic discrete-time system.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Security mechanisms for wireless sensor networks (WSN) face a great challenge due to the restriction of their small sizes and limited energy. Hence, many protocols for WSN are not designed with the consideration of security. Chaotic cryptosystems have the advantages of high security and little cost of time and space, so this paper proposes a secure cluster routing protocol based on chaotic encryption as well as a conventional symmetric encryption scheme. First, a principal-subordinate chaotic function...

In this note we characterize chaotic functions (in the sense of Li and Yorke) with topological entropy zero in terms of the structure of their maximal scrambled sets. In the interim a description of all maximal scrambled sets of these functions is also found.

We consider dynamical systems on a separable metric space containing at least two points. It is proved that weak topological mixing implies generic chaos, but the converse is false. As an application, some results of Piórek are simply reproved.

For a class of quasiperiodically forced time-discrete dynamical systems of two variables (θ,x) ∈ ${T}^{1}\times {\mathbb{R}}_{+}$ with nonpositive Lyapunov exponents we prove the existence of an attractor Γ̅ with the following properties: 1. Γ̅ is the closure of the graph of a function x = ϕ(θ). It attracts Lebesgue-a.e. starting point in ${T}^{1}\times {\mathbb{R}}_{+}$. The set θ:ϕ(θ) ≠ 0 is meager but has full 1-dimensional Lebesgue measure. 2. The omega-limit of Lebesgue-a.e point in ${T}^{1}\times {\mathbb{R}}_{+}$ is $\Gamma \u0305$, but for a residual set of points in ${T}^{1}\times {\mathbb{R}}_{+}$ the omega limit is the...