Temporal dissipative solitons in the Morris-Lecar model with time-delayed feedback.

We study the dynamics and bifurcations of temporal dissipative solitons in an excitable system under time-delayed feedback. As a prototypical model displaying different types of excitability, we use the Morris-Lecar model. In the limit of large delay, soliton like solutions of delay-differential equations can be treated as homoclinic solutions of an equation with an advanced argument. Based on this, we use concepts of classical homoclinic bifurcation theory to study different types of pulse solutions and to explain their dependence on the system parameters. In particular, we show how a homoclinic orbit flip of a single-pulse soliton leads to the destabilization of equidistant multi-pulse solutions and to the emergence of stable pulse packages. It turns out that this transition is induced by a heteroclinic orbit flip in the system without feedback, which is related to the excitability properties of the Morris-Lecar model.

Noise-induced dynamical regimes in a system of globally coupled excitable units.

We study the interplay of global attractive coupling and individual noise in a system of identical active rotators in the excitable regime. Performing a numerical bifurcation analysis of the nonlocal nonlinear Fokker-Planck equation for the thermodynamic limit, we identify a complex bifurcation scenario with regions of different dynamical regimes, including collective oscillations and coexistence of states with different levels of activity. In systems of finite size, this leads to additional dynamical features, such as collective excitability of different types and noise-induced switching and bursting. Moreover, we show how characteristic quantities such as macroscopic and microscopic variability of interspike intervals can depend in a non-monotonous way on the noise level.

Unfavorable Donor Pretransplant APACHE II, SAPS II, and SOFA Scores Are Not Associated With Outcome: Implications for Heart Transplant Donor Selection.

BACKGROUND: The quality of the donor heart and the individual risk of the recipient awaiting heart transplantation are difficult to assess. We investigated whether routinely used intensive care scoring systems can provide additional prognostic information on outcomes after heart transplantation. METHODS: A total of 114 consecutive patients who underwent heart transplantation were included. The Acute Physiology and Chronic Health Evaluation II (APACHE II), the Simplified Acute Physiology Score (SAPS II), and the Sequential Organ Failure Assessment (SOFA) scores were calculated for donors and recipients. Risk factors such as the donor's cause of death, donor's catecholamine use, dialysis status of the recipient, and smoking pattern of the donor and the recipient were assessed. The association of these parameters with mortality, length of stay on the intensive care unit, and need for invasive ventilation was investigated. RESULTS: The median APACHE II score of the donors was 20 (confidence interval [CI], 19-20), the median SAPS II score was 46 (CI, 45-48), and the median SOFA score was 10 (CI, 9-10). In contrast, the median scores of the recipients were as follows: APACHE II, 7 (CI, 6-8); SAPS II, 13 (CI, 12-14); and SOFA, 1 (CI, 1-2). None of the scores as calculated significantly predicted clinical outcome after transplantation. CONCLUSIONS: This study detected no prognostic impact of donor-related risk factors on outcome after heart transplantation. Our findings support the growing practice of also considering organs from donors with high-risk scores for heart transplantation.

Amplitude equations for collective spatio-temporal dynamics in arrays of coupled systems.

We study the coupling induced destabilization in an array of identical oscillators coupled in a ring structure where the number of oscillators in the ring is large. The coupling structure includes different types of interactions with several next neighbors. We derive an amplitude equation of Ginzburg-Landau type, which describes the destabilization of a uniform stationary state and close-by solutions in the limit of a large number of nodes. Studying numerically an example of unidirectionally coupled Duffing oscillators, we observe a coupling induced transition to collective spatio-temporal chaos, which can be understood using the derived amplitude equations.

Stationary patterns of coherence and incoherence in two-dimensional arrays of non-locally-coupled phase oscillators.

Recently, it has been shown that large arrays of identical oscillators with nonlocal coupling can have a remarkable type of solutions that display a stationary macroscopic pattern of coexisting regions with coherent and incoherent motions, often called chimera states. Here, we present a detailed numerical study of the appearance of such solutions in two-dimensional arrays of coupled phase oscillators. We discover a variety of stationary patterns, including circular spots, stripe patterns, and patterns of multiple spirals. Here, stationarity means that, for increasing system size, the locally averaged phase distributions tend to the stationary profile given by the corresponding thermodynamic limit equation.

Spectral properties of chimera states.

Chimera states are particular trajectories in systems of phase oscillators with nonlocal coupling that display a spatiotemporal pattern of coherent and incoherent motion. We present here a detailed analysis of the spectral properties for such trajectories. First, we study numerically their Lyapunov spectrum and its behavior for an increasing number of oscillators. The spectra demonstrate the hyperchaotic nature of the chimera states and show a correspondence of the Lyapunov dimension with the number of incoherent oscillators. Then, we pass to the thermodynamic limit equation and present an analytic approach to the spectrum of a corresponding linearized evolution operator. We show that, in this setting, the chimera state is neutrally stable and that the continuous spectrum coincides with the limit of the hyperchaotic Lyapunov spectrum obtained for the finite size systems.

Routes to complex dynamics in a ring of unidirectionally coupled systems.

We study the dynamics of a ring of unidirectionally coupled autonomous Duffing oscillators. Starting from a situation where the individual oscillator without coupling has only trivial equilibrium dynamics, the coupling induces complicated transitions to periodic, quasiperiodic, chaotic, and hyperchaotic behavior. We study these transitions in detail for small and large numbers of oscillators. Particular attention is paid to the role of unstable periodic solutions for the appearance of chaotic rotating waves, spatiotemporal structures, and the Eckhaus effect for a large number of oscillators. Our analytical and numerical results are confirmed by a simple experiment based on the electronic implementation of coupled Duffing oscillators.

Semiconductor laser under resonant feedback from a Fabry-Perot resonator: Stability of continuous-wave operation.

We study the continuous-wave (cw) operation of a semiconductor laser subject to optical feedback from a Fabry-Perot resonator in a case where the emission is resonant to a reflection minimum of the resonator. This configuration is treated in the framework of Lang-Kobayashi equations. The nature of bifurcations and the stability of steady state solutions is analyzed in terms of the dependence on magnitude and phase of the feedback. In contrast to conventional optical feedback from a single mirror, the locus of external cavity modes is not elliptic but represents a tilted eight with possible satellite bubbles. Below a critical feedback strength, which is analytically given, only one single mode exists representing the completely unchanged cw emission of the laser. In this weak-feedback regime, the feedback phase allows noninvasive control of the cw emission and a tailoring of its small-signal response within wide limits. The results obtained are a prototype for all-optical realizations of delayed feedback control.

[Diabetic nephropathy in type II diabetes: effect of metabolic control and blood pressure on its development and course]. / Diabetische Nephropathie bei Typ-II-Diabetes. Einfluss von Stoffwechselkontrolle und Blutdruck auf Entwicklung und Verlauf.

The influence of metabolic control and blood pressure on the onset and course of clinical nephropathy (persistent proteinuria) was investigated in 63 type II diabetics with persistent proteinuria and a corresponding group without proteinuria. Diabetics with a later onset of persistent proteinuria had, even in the pre-proteinuria stage, higher blood pressures than diabetics without proteinuria. There was an inverse relationship between blood pressure and the interval between the diagnosis of diabetes and the onset of persistent proteinuria. There was no difference in metabolic control between diabetics with and those without later development of persistent proteinuria. However, for patients with clinical nephropathy there was a weak inverse correlation between blood pressure levels during the preproteinuric stage, on one hand, and the interval between diabetes diagnosis and onset of persistent proteinuria, on the other. Poor metabolic control and hypertension during the proteinuric stage were associated with rapid deterioration of renal function.