We study the chaotic attractors of a delay differential equation. The dimension of several attractors computed directly from the definition agrees to experimental resolution ~vith the dimension computed from the spectrum of Lyapunov exponents according to a conjecture of Kaplan and Yorke. Assuming this conjecture to be valid, as the delay parameter is varied, from computations of the spectrum o...

We introduce a simple geometrical two-dimensional continued fraction algorithm inspired from dynamical renormalization. We prove that the algorithm is weakly convergent, and that the associated transformation admits an ergodic absolutely continuous invariant probability measure. Following Lagarias, its Lyapunov exponents are related to the approximation exponents which measure the diophantine q...

In this paper, we study the Lyapunov exponents of a micro chaotic mixer to understand the mixing effectiveness under different operating parameters. A simple kinematic micro mixer model is used for the simulated flow visualization and then for the computation of Lyapunov exponents using two different numerical methods. These two methods generate consistent result to corroborate the existence of...

In this paper, we discuss the dynamical properties of a chemical reactor model including Lyapunov exponents, bifurcation, stability of equilibrium and chaotic attractors as well as necessary conditions for this system to generate chaos. We study the synchronization of chemical reactors model via sliding mode control scheme. The stability of proposed method is proved by Barbalate’s lemma. Numeri...

We study the Lyapunov exponents for a moving, charged particle in a two-dimensional Lorentz gas with randomly placed, non-overlapping hard disk scatterers placed in a thermostatted electric field, ~ E. The low density values of the Lyapunov exponents have been calculated with the use of an extended Lorentz-Boltzmann equation. In this paper we develop a method to extend these results to higher d...

By studying the integrated density of states, we prove the existence of Lyapunov exponents and the Thouless formula for the Schrödinger operator −d2/dx2 + cos xν with 0 < ν < 1 on L2[0,∞). This yields an explicit formula for these Lyapunov exponents. By applying rank one perturbation theory, we also obtain some spectral consequences.