Hilda A. Cerdeira

Experimental investigation of partial synchronization in coupled chaotic oscillators.

The dynamical behavior of a ring of six diffusively coupled Rössler circuits, with different coupling schemes, is experimentally and numerically investigated using the coupling strength as a control parameter. The ring shows partial synchronization and all the five patterns predicted analyzing the symmetries of the ring are obtained experimentally. To compare with the experiment, the ring has been integrated numerically and the results are in good qualitative agreement with the experimental ones. The results are analyzed through the graphs generated plotting the y variable of the ith circuit versus the variable y of the jth circuit. As an auxiliary tool to identify numerically the behavior of the oscillators, the three largest Lyapunov exponents of the ring are obtained.

Order in the turbulent phase of globally coupled maps

Abstract The broad peaks seen in the power spectra of the mean field in a globally coupled map system indicate a subtle coherence between the elements, even in the “turbulent” phase. These peaks are investigated in detail with respect to the number of elements coupled, nonlinearity and global coupling strengths. We find that this roughly periodic behavior also appears in the probability distribution of the mapping, which is therefore not invariant. We also find that these peaks are determined by two distinct components: effective renormalization of the nonlinearity parameter in the local mappings, and the strength of the mean field interaction term. Finally, we demonstrate the influence of background noise on the peaks, which is quite counterintuitive, as they become sharper with increase in strength of the noise, up to a certain critical noise strength.

Transition to complete synchronization in phase-coupled oscillators with nearest neighbor coupling

We investigate synchronization in a Kuramoto-like model with nearest neighbor coupling. Upon analyzing the behavior of individual oscillators at the onset of complete synchronization, we show that the time interval between bursts in the time dependence of the frequencies of the oscillators exhibits universal scaling and blows up at the critical coupling strength. We also bring out a key mechanism that leads to phase locking. Finally, we deduce forms for the phases and frequencies at the onset of complete synchronization.

FRACTAL PROPERTIES OF DNA WALKS

We describe two dimensional DNA walks, and analyze their fractal properties. We show results for the complete genome of S. cerevisiae. We find that the mean square deviation of the walks is superdifussive, corresponding to a fractal structure of dimension lower than two. Furthermore, the coding part of the genome seems to have smaller fractal dimension, and longer correlations, than noncoding parts.

Determination of the critical coupling for oscillators in a ring

We study a model of coupled oscillators with bidirectional first nearest neighbors coupling with periodic boundary conditions. We show that a stable phase-locked solution is decided by the oscillators at the borders between the major clusters, which merge to form a larger one of all oscillators at the stage of complete synchronization. We are able to locate these four oscillators depending only on the set of the initial frequencies. Using these results plus an educated guess (supported by numerical findings) of the functional dependence of the corrections due to periodic boundary conditions, we are able to obtain a formula for the critical coupling, at which the complete synchronization state occurs. Such formula fits well in very good accuracy with the results that come from numerical simulations. This also helps to determine the sizes of the major clusters in the vicinity of the stage of full synchronization.

Chaotic instability of currents in a reverse biased multilayered structure

A new principle to generate chaotic signals using the phenomenon of charge avalanche multiplication and internal feedback in multilayered semiconductor structures is suggested. Linear and nonlinear theories for the self-oscillations are developed and existence of the chaotic regime with fast decay of correlations is proven.

Effective Fokker-Planck equation for birhythmic modified van der Pol oscillator

We present an explicit solution based on the phase-amplitude approximation of the Fokker-Planck equation associated with the Langevin equation of the birhythmic modified van der Pol system. The solution enables us to derive probability distributions analytically as well as the activation energies associated with switching between the coexisting different attractors that characterize the birhythmic system. Comparing analytical and numerical results we find good agreement when the frequencies of both attractors are equal, while the predictions of the analytic estimates deteriorate when the two frequencies depart. Under the effect of noise, the two states that characterize the birhythmic system can merge, inasmuch as the parameter plane of the birhythmic solutions is found to shrink when the noise intensity increases. The solution of the Fokker-Planck equation shows that in the birhythmic region, the two attractors are characterized by very different probabilities of finding the system in such a state. The probability becomes comparable only for a narrow range of the control parameters, thus the two limit cycles have properties in close analogy with the thermodynamic phases.

Synchronization in a chain of nearest neighbors coupled oscillators with fixed ends

We investigate a system of coupled phase oscillators with nearest neighbors coupling in a chain with fixed ends. We find that the system synchronizes to a common value of the time-averaged frequency, which depends on the initial phases of the oscillators at the ends of the chain. This time-averaged frequency decays as the coupling strength increases. Near the transition to the frozen state, the time-averaged frequency has a power law behavior as a function of the coupling strength, with synchronized time-averaged frequency equal to zero. Associated with this power law, there is an increase in phases of each oscillator with 2pi jumps with a scaling law of the elapsed time between jumps. During the interval between the full frequency synchronization and the transition to the frozen state, the maximum Lyapunov exponent indicates quasiperiodicity. Time series analysis of the oscillators frequency shows this quasiperiodicity, as the coupling strength increases.

Current oscillations in avalanche particle detectors with p-n-i-p-n-structure

We describe the model of an avalanche high energy particle detector consisting of two p-n-junctions, connected through an intrinsic semiconductor with a reverse biased voltage applied. We show that this detector is able to generate the oscillatory response on the single particle passage through the structure. The possibility of oscillations leading to chaotic behavior is pointed out.

Nontrivial dynamics induced by a nonlinear Jaynes-Cummings Hamiltonian

Abstract The addition of a nonlinear term to the Jaynes-Cummings Hamiltonian induced a nontrivial discrete dynamics for the number of possible transitions of a given order, represented by a Fibonacci series. We describe the physics of the problem in terms of relevant operators which close a semi-Lie algebra under commutation with the Hamiltonian and therefore extending the generalized Bloch equations, already obtained for the linear case, to the nonlinear one. The initial conditions as well as a thermodynamical treatmetn of the problem is analyzed via the maximum entropy principle density operator. Finally, a generalized solution for the time-independent case is obtained and the solution for the field in a thermal state is recovered.