Non-linearity is essential for occurrence of chaos in dynamical system. The size of phase space and formation of attractors are much dependent on the setting of nonlinear function and parameters. In this paper, a three-variable dynamical system is controlled by different nonlinear function thus a class of chaotic system is presented, the Hamilton function is calculated to find the statistical dynamical property of the improved dynamical systems composed of hidden attractors. The standard dynamical...

In this article a method is presented to find systematically the domain of attraction (DOA) of hybrid non-linear systems. It has already been shown that there exists a sequence of special kind of Lyapunov functions $V_n$ in a rational functional form approximating a maximal Lyapunov function $V_M$ that can be used to find an estimation for the DOA. Based on this idea, an improved method has been developed and implemented in a Mathematica-package to find such Lyapunov functions $V_n$ for a class of hybrid (piecewise...

This survey is an introduction to some of the methods, techniques and concepts from algebraic topology and related areas (homotopy theory, shape theory) which can be fruitfully applied to study problems concerning continuous dynamical systems. To this end two instances which exemplify the interaction between topology and dynamics are considered, namely, Conley’s index theory and the study of some properties of certain attractors.