Fuzzy Control of Chaos

We introduce the idea of the fuzzy control of chaos: we show how fuzzy logic can be applied to the control of chaos, and provide an example of fuzzy control used to control chaos in Chua's circuit

Optimum PID Control of Multi-wing Attractors in A Family of Lorenz-like Chaotic Systems

Multi-wing chaotic attractors are highly complex nonlinear dynamical systems with higher number of index-2 equilibrium points. Due to the presence of several equilibrium points, randomness of the state time series for these multi-wing chaotic systems is higher than that of the conventional double wing chaotic attractors. A real coded Genetic Algorithm (GA) based global optimization framework has been presented in this paper, to design optimum PID controllers so as to control the state trajectories of three different multi-wing Lorenz like chaotic systems viz. Lu, Rucklidge and Sprott-1 system.Comment: 6 pages, 21 figures; 2012 Third International Conference on Computing, Communication and Networking Technologies (ICCCNT'12), July 2012, Coimbator

From large deviations to semidistances of transport and mixing: coherence analysis for finite Lagrangian data

One way to analyze complicated non-autonomous flows is through trying to understand their transport behavior. In a quantitative, set-oriented approach to transport and mixing, finite time coherent sets play an important role. These are time-parametrized families of sets with unlikely transport to and from their surroundings under small or vanishing random perturbations of the dynamics. Here we propose, as a measure of transport and mixing for purely advective (i.e., deterministic) flows, (semi)distances that arise under vanishing perturbations in the sense of large deviations. Analogously, for given finite Lagrangian trajectory data we derive a discrete-time and space semidistance that comes from the "best" approximation of the randomly perturbed process conditioned on this limited information of the deterministic flow. It can be computed as shortest path in a graph with time-dependent weights. Furthermore, we argue that coherent sets are regions of maximal farness in terms of transport and mixing, hence they occur as extremal regions on a spanning structure of the state space under this semidistance---in fact, under any distance measure arising from the physical notion of transport. Based on this notion we develop a tool to analyze the state space (or the finite trajectory data at hand) and identify coherent regions. We validate our approach on idealized prototypical examples and well-studied standard cases.Comment: J Nonlinear Sci, 201

Chaotic vibrations and strong scars

This article aims at popularizing some aspects of "quantum chaos", in particular the study of eigenmodes of classically chaotic systems, in the semiclassical (or high frequency) limit