Sound synchronization of bubble trains in a viscous fluid : Experiment and modeling

Acknowledgements: We thank the São Paulo State Agency FAPESP and the Federal Brazilian Agency CNPq for the financial support. M.S.B. acknowledges EPSRC Grant No. EP/IO32606/1.Peer reviewedPublisher PD

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

Bifurcations, Chaos, Controlling and Synchronization of Certain Nonlinear Oscillators

In this set of lectures, we review briefly some of the recent developments in the study of the chaotic dynamics of nonlinear oscillators, particularly of damped and driven type. By taking a representative set of examples such as the Duffing, Bonhoeffer-van der Pol and MLC circuit oscillators, we briefly explain the various bifurcations and chaos phenomena associated with these systems. We use numerical and analytical as well as analogue simulation methods to study these systems. Then we point out how controlling of chaotic motions can be effected by algorithmic procedures requiring minimal perturbations. Finally we briefly discuss how synchronization of identically evolving chaotic systems can be achieved and how they can be used in secure communications.Comment: 31 pages (24 figures) LaTeX. To appear Springer Lecture Notes in Physics Please Lakshmanan for figures (e-mail: [email protected]