Probability density adjoint for sensitivity analysis of the Mean of Chaos

Sensitivity analysis, especially adjoint based sensitivity analysis, is a powerful tool for engineering design which allows for the efficient computation of sensitivities with respect to many parameters. However, these methods break down when used to compute sensitivities of long-time averaged quantities in chaotic dynamical systems. The following paper presents a new method for sensitivity analysis of {\em ergodic} chaotic dynamical systems, the density adjoint method. The method involves solving the governing equations for the system's invariant measure and its adjoint on the system's attractor manifold rather than in phase-space. This new approach is derived for and demonstrated on one-dimensional chaotic maps and the three-dimensional Lorenz system. It is found that the density adjoint computes very finely detailed adjoint distributions and accurate sensitivities, but suffers from large computational costs.Comment: 29 pages, 27 figure

Phase synchronization in time-delay systems

Though the notion of phase synchronization has been well studied in chaotic dynamical systems without delay, it has not been realized yet in chaotic time-delay systems exhibiting non-phase coherent hyperchaotic attractors. In this article we report the first identification of phase synchronization in coupled time-delay systems exhibiting hyperchaotic attractor. We show that there is a transition from non-synchronized behavior to phase and then to generalized synchronization as a function of coupling strength. These transitions are characterized by recurrence quantification analysis, by phase differences based on a new transformation of the attractors and also by the changes in the Lyapunov exponents. We have found these transitions in coupled piece-wise linear and in Mackey-Glass time-delay systems.Comment: 4 pages, 3 Figures (To appear in Physical Review E Rapid Communication

DYNAMICAL AND STATISTICAL ANALYSIS OF A NEW LOZI FUNCTION FOR RANDOM NUMBERS GENERATION

International audienceThis paper presents the first results of the statistical and dynamical analysis of a new function showing random properties firstly proposed by Lozi. The phase plane analysis via the critical lines tool allowed to delimit analytically the holes in the chaotic attractor and to follow their evolution. In addition, the results of the statistical NIST tests for pseudo-randomness showed to be successful and significantly improved after an under-sampling of the output signal