Results

**1 - 6**of**6**### In the Phase Diagram Fig. 3.1, the Attractor Seems Not Only to Visit the Vicinity of

"... close to ffl PB . Consider as an initial condition a pulse with a finite perturbation in its tail, (T = 0 in fig. 3.4 and fig. 3.5). As one can readily see, the perturbation rapidly grows (T = 250) creating two pulses moving in opposite directions (T = 1000). As time increases, the rightmost pulse ..."

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close to ffl PB . Consider as an initial condition a pulse with a finite perturbation in its tail, (T = 0 in fig. 3.4 and fig. 3.5). As one can readily see, the perturbation rapidly grows (T = 250) creating two pulses moving in opposite directions (T = 1000). As time increases, the rightmost pulse moves away from the remaining pattern and does not interact any further. The pattern moving with apparently constant velocity to the left develops more oscillations (T = 3000 \Gamma 9000) forming a front connecting YA and a neighborhood of the unstable YC . The important dynamical consequence of this structure is that behind the front, pulse-like waves are emitted constantly in both directions. While the ones traveling in the direction of the original excitation merge the leading front, a sequence of pulses is observed to move in the

### Global Bifurcations and Chaotic Dynamics in Physical Applications

, 1997

"... Zimmermann, M. G. 1997. Global Bifurcations and Chaotic Dynamics in Physical Applications. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 279. 48 pp. Uppsala. ISBN 91-554-3972-1. The aim of this work has been to analyse glo ..."

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Zimmermann, M. G. 1997. Global Bifurcations and Chaotic Dynamics in Physical Applications. Acta Universitatis Upsaliensis. Comprehensive Summaries of Uppsala Dissertations from the Faculty of Science and Technology 279. 48 pp. Uppsala. ISBN 91-554-3972-1. The aim of this work has been to analyse global bifurcations arising in a laser with injected signal and in a catalytic reaction on a surface of Pt, from the point of view of dynamical systems theory. The 3-dimensional ordinary differential equation which models the laser was found to contain a homoclinic orbit to a saddle-focus equilibrium, what corresponds to the Sil'nikov phenomenon. It is well known that under certain eigenvalue relationship, this global bifurcation displays chaotic dynamics. In this problem the fixed point was also involved in a Hopf/saddle-node local bifurcation. The interaction of the Sil'nikov phenomenon and the saddle-node bifurcation was studied by constructing a geometrical model. It was determined that a...

### Red Queen strange attractors in host–parasite replicator gene-for-gene coevolution

, 2006

"... We study a continuous time model describing gene-for-gene, host–parasite interactions among self-replicating macromolecules evolving in both neutral and rugged fitness landscapes. Our model considers polymorphic genotypic populations of sequences with 3 bits undergoing mutation and incorporating a ‘ ..."

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We study a continuous time model describing gene-for-gene, host–parasite interactions among self-replicating macromolecules evolving in both neutral and rugged fitness landscapes. Our model considers polymorphic genotypic populations of sequences with 3 bits undergoing mutation and incorporating a ‘‘type II’ ’ non-linear functional response in the host–parasite interaction. We show, for both fitness landscapes, a wide range of chaotic coevolutionary dynamics governed by Red Queen strange attractors. The analysis of a rugged fitness landscape for parasite sequences reveals that fittest genotypes achieve lower stationary concentration values, as opposed to the flattest ones, which undergo a higher stationary concentration. Our model also shows that the increase of parasites pressure (higher self-replication and mutation rates) generically involves a simplification of the host–parasite dynamical behavior, involving the transition from a chaotic to an ordered coevolutionary phase. Moreover, the same transition can also be found when hosts ‘‘run’’ faster through the hypercube. Our results, in agreement with previous studies in host–parasite coevolution, suggest that chaos might be common in coevolutionary dynamics of changing self-replicating entities undergoing a host–parasite ecology.

### Nonlinear Dynamics of Current-Modulated Multitransverse Mode Vertical-Cavity Surface-Emitting Lasers

"... An analysis of the nonlinear dynamics of current modulated weakly index-guided VCSELs in a multi-transverse mode regime is performed by using a model that takes into account all the transverse modes supported bythe waveguide. Nonlinear dynamical behavior is studied when applying current modulation ..."

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An analysis of the nonlinear dynamics of current modulated weakly index-guided VCSELs in a multi-transverse mode regime is performed by using a model that takes into account all the transverse modes supported bythe waveguide. Nonlinear dynamical behavior is studied when applying current modulation of high frequency and large modulation depth. Chaotic behavior is obtained in the multitransverse mode regime due to transverse mode competition. Chaotic operation is such that multistability of the chaos-chaos type is observed. Injection of appropriate optical pulses can switch between different stable chaotic solutions. The case of a VCSEL in which the fundamental mode is selected is also analysed. Nonlinear dynamics of the single mode VCSEL is such that the chaotic behavior is not present for the considered range of current modulation amplitudes and frequencies. Only periodic behaviors are observed, in such away that multistability of different periodic solutions also appears. Switching between different stable periodic solutions also appears when appropriate external optical pulses are injected. Finally,weshow that spontaneous emission noise increases the numberofavailable channels in chaotic optical communication systems in which frequency division multiplexing with multi-transverse mode VCSELs is used.

### Influence of observational noise on the recurrence quantification analysis

"... In this paper, we estimate the errors due to observational noise on the recurrence quantification analysis (RQA). Based on this estimation, we present ways to minimize these errors. We give a criterion to choose the threshold ε needed for the optimal computation of the recurrence plot (RP). One impo ..."

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In this paper, we estimate the errors due to observational noise on the recurrence quantification analysis (RQA). Based on this estimation, we present ways to minimize these errors. We give a criterion to choose the threshold ε needed for the optimal computation of the recurrence plot (RP). One important point is to show the limits of interpretability of the results of the RQA if it is applied to measured time series. We show that even though the RQA is very susceptible to observational noise, it can yield reliable results for an optimal choice of ε if the noise level is not too high. We apply the results to typical models, such as white noise, the logistic map and the Lorenz system, and to experimental laser data.