Correlation dimension is attained from the correlations between random points on the attractor. For an one dimensional discrete dynamical system with initial condition, x0 Lyapunov exponent (x0) is defined. The Henon map is a discrete time dynamical system. In logistic map is quadratic. The Kaplan-Yorke map is a discrete -time dynamical system. A nnr ( ) subroutine is written to find all mean n...

The study of temporal chaos in low-dimensional systems, some of which can be described by low-dimensional maps @1,2#, was extremely beneficial for the understanding of turbulence. In 1984 coupled map lattices ~CMLs! were introduced into the physical literature as a tool for studying spatiotemporal chaos in spatially extended, i.e., highdimensional systems @3#. They consist of spatially coupled ...

One-dimensional differential equations dy/dt = f (t, y) that are periodic in t arise in many areas of applied mathematics. The attracting and repelling periodic solutions and their bifurcations are the key qualitative features that determine the observed behavior of the system being modeled. One quickly finds that the low dimensional character of the problem conceals difficulties that in practi...