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modes Fixed points appear and disappear pairwise in saddle node bifurcations, ie one of them, the anti-mode, is an unstable saddle point Generally, moving upwards along a vertical line, the first intersection is a mode, followed by an anti-mode, then again a mode, etc and the last intersection is a mode again Stability analysis can tell us whether a mode is stable, but anti-modes are always unstable In Figure 35 the amplitude of oscillations clearly reflects the Lorentzian filter profile Inset (c) shows two distinct islands of fixed points, ie a global bistability , induced by the filter Roughly speaking, the system here can choose between one of two operational states; either adjust its operation frequency in response to the maximum feedback, or ignore the filter resonance and operate as a laser with weak feedback Note that the filter-resonance ECMs have higher intensity than the weak-feedback ECMs.

reveal an atrial tachycardia from the pulmonary vein, which deteriorates into atrial brillation. There are a number of techniques that have been described for ablation of atrial brillation, but most center on ablation of the pulmonary vein region. Initially, trigger sites within the pulmonary vein were targeted for ablation. However, because of the risk of pulmonary vein stenosis and recurrent arrhythmias from other sites, the strategy shifted to making a circumferential lesion around the pulmonary veins in an attempt to isolate rapid activity within the veins from the rest of the atrium (Fig. 13.4) by a series of point-by-point lesions. Figure 13.5 shows an isolated pulmonary vein, with rapid depolarizations within the pulmonary vein that are not conducted to the atria. The patient s atria are activated normally by the sinus node. Although isolating the pulmonary veins is effective in some patients, it is now appreciated that sites within the left atrium may be important for the development or maintenance of atrial brillation in a large number of patients. In addition, regions of high-frequency atrial activity often referred to as complex fractionated atrial electrograms or CFAEs have also been targets for ablation, particularly in those patients with persistent atrial brillation. Although de nitions vary, CFAEs are characterized by short cycle lengths (< 120 ms)

This is a consequence of the phase-amplitude coupling described by [13], which implies higher intensities on red shifts from the laser operation frequency The opposite effect is seen in inset (a), where the islands of ECMs are just about to separate, but now the weak-feedback ECMs have higher intensity In the next section the dynamical behaviour of a semiconductor laser due to FOF will be studied In this respect, knowledge of the fixed points may provide hints of where attractor orbits are likely to be found and how complex the attractors may get This can be achieved through a combination of studying the temporal behaviour of the laser light intensity, as well as the phase space dynamics of the laser Formally, our delay system is infinite-dimensional, whether the feedback is filtered or not [14].

2

The induced surface charge density needed to satisfy Gauss s law at a perfectly at, perfect conductin metal boundary is e,s = 2E2,x. The surface charge density moves at the phase velocity of the propagating wave to form a linear current density J l = e,sup z. The phase velocity of the propagating surface current is much larger than the velocity of bulk metal conduction electrons at the Fermi level so the surface charge density is not being transported by conduction electrons but by transverse induction of the conduction electrons by the propagating electromagnetic waves.

In practice, however, when looking at the attractors, the dynamics of the system seem to take place effectively in some finite-dimensional phase space This appears to be related to the complexity of the dynamics We therefore propose to introduce the number of fixed points Cplx as a quantitative measure for the complexity the system In case of COF this quantity fluctuates around a value of close to / 1 + 2 with jumps of at most 2 when the pump current is varied Figure 36 shows the function Cplx versus solitary laser frequency for the same FOF case as Figure 35.

Far away from the filter centre frequency, Cplx is a decreasing function with increasing detuning 0 f , but since the number of fixed points is higher in the middle flanks of the filter profile than at the centre, it is a twin peaked function of the detuning From this we expect that the dynamics will in general be higher in complexity at the filter.

As you can see, the last line is our exit(0) syscall. If you d like, go back and modify the shellcode to execute the exit_group() syscall: