Chaotic orbits obeying one isolating integral in a four-dimensional map

One-dimensional map lattices: Synchronization, bifurcations, and chaotic structures.

Chaotic diffusion on periodic orbits: the perturbed Arnold cat map.

Chaotic diffusion on periodic orbits (POs) is studied for the perturbed Arnold cat map on a cylinder, in a range of perturbation parameters corresponding to an extended structural-stability regime of the system on the torus. The diffusion coefficient is calculated, using the following PO formulas: (1). the curvature expansion of the Ruelle zeta function; (2). the average of the PO winding-numbe...

A Novel True Random Number Generator Based on Mouse Movement and a One-Dimensional Chaotic Map

We propose a novel true random number generator using mouse movement and a onedimensional chaotic map. We utilize the x-coordinate of the mouse movement to be the length of an iteration segment of our TRNs and the y-coordinate to be the initial value of this iteration segment. And, when it iterates, we perturb the parameter with the real value produced by the TRNG itself. And we find that the T...

Robustification of a One-Dimensional Generic Sigmoidal Chaotic Map with Application of True Random Bit Generation

The search for generation approaches to robust chaos has received considerable attention due to potential applications in cryptography or secure communications. This paper is of interest regarding a 1-D sigmoidal chaotic map, which has never been distinctly investigated. This paper introduces a generic form of the sigmoidal chaotic map with three terms, i.e., xn+1 = ∓Af NL(Bxn) ± Cxn ± D, where...

Better logic obeying a zero-one law

We study zero-one laws for random graphs. We focus on the following question that was asked by many: Given a graph property P , is there a language of graphs able to express P while obeying the zeroone law? Our results show that on the one hand there is a (regular) language able to express connectivity and k-colorability for any constant k and still obey the zero-one law. On the other hand we s...