Controlling turbulence in coupled map lattice systems using feedback techniques

We report the suppression of spatiotemporal chaos observed in coupled map lattices. Suppression is achieved using different feedback techniques, most of which are applicable to actual experimental situations. Results from application of feedback control to a single chaotic element (single map) are presented to demonstrate similarities in the dynamical response of a single system and an extended system under the influence of external feedback

Birhythmicity induced by perturbing an oscillating electrochemical system

We describe the generation of new limit cycles in electrochemical systems under the influence of external periodic perturbations. For certain specific parameters of a nonharmonic forcing function, two coexisting periodic orbits can be generated from a single limit cycle observed in the unperturbed dynamics. This inception of birhythmicity (bistability) is observed in both simulations and actual experiments involving potentiostatic electrodissolution of copper in an acetate buffer

Time--delay autosynchronization of the spatio-temporal dynamics in resonant tunneling diodes

The double barrier resonant tunneling diode exhibits complex spatio-temporal patterns including low-dimensional chaos when operated in an active external circuit. We demonstrate how autosynchronization by time--delayed feedback control can be used to select and stabilize specific current density patterns in a noninvasive way. We compare the efficiency of different control schemes involving feedback in either local spatial or global degrees of freedom. The numerically obtained Floquet exponents are explained by analytical results from linear stability analysis.Comment: 10 pages, 16 figure

Generalized Chaotic Synchronizationin Coupled Ginzburg-Landau Equations

Generalized synchronization is analyzed in unidirectionally coupled oscillatory systems exhibiting spatiotemporal chaotic behavior described by Ginzburg-Landau equations. Several types of coupling betweenthe systems are analyzed. The largest spatial Lyapunov exponent is proposed as a new characteristic of the state of a distributed system, and its calculation is described for a distributed oscillatory system. Partial generalized synchronization is introduced as a new type of chaotic synchronization in spatially nonuniform distributed systems. The physical mechanisms responsible for the onset of generalized chaotic synchronization in spatially distributed oscillatory systems are elucidated. It is shown that the onset of generalized chaotic synchronization is described by a modified Ginzburg-Landau equation with additional dissipation irrespective of the type of coupling. The effect of noise on the onset of a generalized synchronization regime in coupled distributed systems is analyzed.Comment: 12 page

Stabilizing Unstable Fixed Points Using Derivative Control

We report the stabilization of unstable fixed points (saddles) in model systems exhibiting bistability. Stabilization is achieved using the derivative control strategy proposed in a different context by Biewlaski et al. (Phys. Rev. 1993, A47, 3276). This strategy does not change the location of fixed points in the system, but does alter their stability (eigenvalues), enabling us to stabilize the previously unstable fixed points (saddles). Maintaining the dynamics on the saddle fixed point could be desirable in certain experimental systems