The dominant Lyapunov exponent of a dynamical system measures the average rate at which nearby trajectories of a system diverge. Even though a positive exponent provides evidence for chaotic dynamics and upredictability, there may predictability of the time series over some finite time periods. In this paper one version of a local Lyapunov exponent is defined for a dynamic system perturbed by n...

This paper aims at providing a numerical calculation method of the spectrum of Lyapunov exponents in a four-dimensional impulsive hybrid nonlinear dynamics of a passive compass-gait model under the OGY control approach by means of a controlled hybrid Poincaré map. We present a four-dimensional simplified analytical expression of such hybrid map obtained by linearizing the uncontrolled impulsive...

The presence of positive Lyapunov exponents in a dynamical system is often taken to be equivalent to the chaotic behavior of that system. We construct a Bernoulli toral linked twist map which has positive Lyapunov exponents and local stable and unstable manifolds defined only on a set of measure zero. This is a deterministic dynamical system with the strongest stochastic property, yet it has po...

In this paper, we introduce a new hyperchaotic complex T-system. This system has complex nonlinear behavior which we study its dynamical properties including invariance, equilibria and their stability, Lyapunov exponents, bifurcation, chaotic behavior and chaotic attractors as well as necessary conditions for this system to generate chaos. We discuss the synchronization with certain and uncerta...

Abstract We describe an approach for finding upper bounds on ODE dynamical system’s maximal Lyapunov exponent (LE) among all trajectories in a specified set. A minimisation problem is formulated whose infimum equal to the LE, provided that of interest remain compact The over auxiliary functions are defined state space and subject pointwise inequality. In polynomial case—i.e. when ODE’s right-ha...

The emergence of chaotic motion is discussed for hard-point like and soft collisions between two particles in a one-dimensional box. It is known that ergodicity may be obtained in hard-point like collisions for specific mass ratios gamma=m(2)/m(1) of the two particles and that Lyapunov exponents are zero. However, if a Yukawa interaction between the particles is introduced, we show analytically...