Showing papers by "Stefano Boccaletti published in 1998"

The control of chaos: theoretical schemes and experimental realizations

Abstract: Controlling chaos is a process wherein an unstable periodic orbit embedded in a chaotic attractor is stabilized by means of tiny perturbations of the system. These perturbations imply goal oriented feedback techniques which act either on the state variables of the system or on the control parameters. We review some theoretical schemes and experimental implementations for the control of chaos.

Weak Synchronization of Chaotic Coupled Map Lattices

Abstract: Phase synchronized states can emerge in the collective behavior of an ensemble of chaotic coupled map lattices, due to a mean field interaction. This type of interaction is responsible for synchronized chaotic global activity of the lattices, while the local activity of each map remains unsynchronized. The resulting collective dynamics is called ``weak synchronization.'' The transition to such a state is characterized in an ensemble of one-dimensional lattices of logistic maps, in terms of the distance in phase among the different lattices. Its robustness against a small difference in the map parameters is proved. We show that this phenomenon can be associated with pattern formation.

Control of amplitude turbulence in delayed dynamical systems

Abstract: An experiment on Benard–Marangoni time-dependent convection shows evidence of an amplitude turbulent regime in the temperature signal which is modeled by a delayed dynamical system. Application of a control procedure, which perturbs the value of the delay time, leads to the control of such dynamical regime, by suppression of phase defects and stabilization of the regular oscillations. The control technique is robust against the presence of large amounts of noise.

Method for the adaptive synchronization of chaotic systems and data transmission system using said method

Abstract: A method for the transmission of information from a transmitter (1) to a receiver (3) is described, in which the transmitter and the receiver each comprise a dynamic system [X ˙1=f(X1, µ); X ˙3=f (X3, µ) ], said two systems being able to be synchronized with each other; a signal (y 3) relating to one of the variables of one of said systems is exchanged between said two dynamic systems; and the information to be transmitted is coded in the form of a disturbance in one of the variables of the system of the transmitter. Characteristically the transmitter comprises: a first and a second dynamic system [X ˙1=f (X1, CL) ; X ˙2=f (X2 r CL)] ] described by identical equations; the receiver (3) transmits to the transmitter (1) a signal (y 3) relating to one of the variables of the dynamic system of the receiver, which signal replaces the corresponding variable (y 2) of the second dynamic system of the transmitter in order to synchronize the second dynamic system of the transmitter with the dynamic system of the receiver; the transmitter (1) sends to the receiver (3) a signal (U(t)) which is a function of the difference between two corresponding variables (x1 (t), x2 (t)) of the first and the second dynamic system of the transmitter; the signal (y 3) which the receiver sends to the transmitter (1) is interrupted for interruption time intervals (To) greater than a decorrelation time of the dynamic systems of the transmitter and the receiver.

Discrimination of deterministic dynamics in the spontaneous activity of the human brain cortex

Abstract: We apply a new strategy to isolate cortical rhythms as deterministic signals and discuss several related topics. Extraction of the relevant signal from the original data is achieved by a novel use of the localized ltering action of the wavelet transform. Alternative nonlinear data analysis tools are used to test the validity of the procedure. In the case of neuromagnetic signals measured on the occipital cortex of a normal subject, we demonstrate the existence of a deterministic activity within the -band (8{12 Hz). The study of the brain bioelectrical activities in terms of deterministic nonlinear dynamics is quite recent (1)-(3). Perspectives of clinical use of the nonlinear tools range from an augmented predictive classication of Alzheimer's desease (4) to the possibility of controlling epileptic activity (5). However, the nonstationarity of the brain states plus the poor Signal-to-Noise Ratio (SNR) due to the large amount of brain processes active at the same time have forbidden so far a generally accepted procedure to estimate suitable indicators (2), (6), (7). Whence the need for a suitably tailored lter able to extract the activity under study to avoid contamination between noise and bioelectrical activities while maintaining a sucient number of data to perform indicator calculations. The reason for this communication is twofold. We apply for the rst time a novel ltering technique based on the local features of the wavelet transformation (8) and, second, we propose a procedure for brain signal processing, making use of available nonlinear tests. The procedure here suggested estimates the presence of determinism in a magnetoencephalo- gram using the newly developed test (9), then, whenever allowed, it calculates the correlation dimensions (CD) (10) and tests the validity of the calculation. We will show that, while the measured signal contains deterministic activity, it is not possible to reasonably estimate the CD, for which we nd, however, an upper bound of 7.