Is one dimensional Poincaré map sufficient to describe the chaotic dynamics of a three dimensional system?

A three-dimensional optical model to describe the optical function of the keratoconus eye

This article has no abstract.

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

Statistical characteristics of the Poincaré return times for a one - dimensional nonhyperbolic map

Characteristics of the Poincaré return times are considered in a one-dimensional cubic map with a chaotic nonhyperbolic attractor. Two approaches, local one (Kac’s theorem) and global one related with the AP-dimension estimation of return times, are used. The return times characteristics are studied in the presence of external noise. The characteristics of Poincaré recurrences are compared with...

Parameter Estimation of a Class One-Dimensional Discrete Chaotic System

It is of vital importance to exactly estimate the unknown parameters of chaotic systems in chaos control and synchronization. In this paper, we present a method for estimating one-dimensional discrete chaotic system based on mean value method MVM . It is proposed by exploiting the ergodic and synchronization features of chaos. It can effectively estimate the parameter value, and it is more exac...

Projective Synchronization of a Modified Three-Dimensional Chaotic Finance System

This article mainly concerns projective synchronization (PS) of a modified chaotic finance system. PS with both identical and different scaling factors between two identical chaotic systems is realized. In addition, the PS of modified chaotic finance system with unknown parameters including the unknown coefficients of nonlinear terms is studied by using adaptive control. Numerical simulations a...