Chaotic pulses for discrete reaction diffusion systems

Existence and dynamics of chaotic pulses on a one-dimensional lattice are discussed. Traveling pulses arise typically in reaction diffusion systems like the FitzHugh-Nagumo equations. Such pulses annihilate when they collide with each other. A new type of traveling pulse has been found recently in many systems where pulses bounce off like elastic balls. We consider the behavior of such a localized pattern on one-dimensional lattice, i.e., an infinite system of ODEs with nearest interaction of diffusive type. Besides the usual standing and traveling pulses, a new type of localized pattern, which moves chaotically on a lattice, is found numerically. Employing the strength of diffusive interaction as a bifurcation parameter, it is found that the route from standing pulse to chaotic pulse is of intermittent type. If two chaotic pulses collide with appropriate timing, they form a periodic oscillating pulse called a molecular pulse. Interaction among many chaotic pulses is also studied numerically

Photo-excited semiconductor superlattices as constrained excitable media: Motion of dipole domains and current self-oscillations

A model for charge transport in undoped, photo-excited semiconductor superlattices, which includes the dependence of the electron-hole recombination on the electric field and on the photo-excitation intensity through the field-dependent recombination coefficient, is proposed and analyzed. Under dc voltage bias and high photo-excitation intensities, there appear self-sustained oscillations of the current due to a repeated homogeneous nucleation of a number of charge dipole waves inside the superlattice. In contrast to the case of a constant recombination coefficient, nucleated dipole waves can split for a field-dependent recombination coefficient in two oppositely moving dipoles. The key for understanding these unusual properties is that these superlattices have a unique static electric-field domain. At the same time, their dynamical behavior is akin to the one of an extended excitable system: an appropriate finite disturbance of the unique stable fixed point may cause a large excursion in phase space before returning to the stable state and trigger pulses and wave trains. The voltage bias constraint causes new waves to be nucleated when old ones reach the contact.Comment: 19 pages, 8 figures, to appear in Phys. Rev.

Nonlinear physics of electrical wave propagation in the heart: a review

The beating of the heart is a synchronized contraction of muscle cells (myocytes) that are triggered by a periodic sequence of electrical waves (action potentials) originating in the sino-atrial node and propagating over the atria and the ventricles. Cardiac arrhythmias like atrial and ventricular fibrillation (AF,VF) or ventricular tachycardia (VT) are caused by disruptions and instabilities of these electrical excitations, that lead to the emergence of rotating waves (VT) and turbulent wave patterns (AF,VF). Numerous simulation and experimental studies during the last 20 years have addressed these topics. In this review we focus on the nonlinear dynamics of wave propagation in the heart with an emphasis on the theory of pulses, spirals and scroll waves and their instabilities in excitable media and their application to cardiac modeling. After an introduction into electrophysiological models for action potential propagation, the modeling and analysis of spatiotemporal alternans, spiral and scroll meandering, spiral breakup and scroll wave instabilities like negative line tension and sproing are reviewed in depth and discussed with emphasis on their impact in cardiac arrhythmias.Peer ReviewedPreprin

Negative tension of scroll wave filaments and turbulence in three-dimensional excitable media and application in cardiac dynamics

Scroll waves are vortices that occur in three-dimensional excitable media. Scroll waves have been observed in a variety of systems including cardiac tissue, where they are associated with cardiac arrhythmias. The disorganization of scroll waves into chaotic behavior is thought to be the mechanism of ventricular fibrillation, whose lethality is widely known. One possible mechanism for this process of scroll wave instability is negative filament tension. It was discovered in 1987 in a simple two variables model of an excitable medium. Since that time, negative filament tension of scroll waves and the resulting complex, often turbulent dynamics was studied in many generic models of excitable media as well as in physiologically realistic models of cardiac tissue. In this article, we review the work in this area from the first simulations in FitzHugh-Nagumo type models to recent studies involving detailed ionic models of cardiac tissue. We discuss the relation of negative filament tension and tissue excitability and the effects of discreteness in the tissue on the filament tension. Finally, we consider the application of the negative tension mechanism to computational cardiology, where it may be regarded as a fundamental mechanism that explains differences in the onset of arrhythmias in thin and thick tissue

Excitable media in open and closed chaotic flows

We investigate the response of an excitable medium to a localized perturbation in the presence of a two-dimensional smooth chaotic flow. Two distinct types of flows are numerically considered: open and closed. For both of them three distinct regimes are found, depending on the relative strengths of the stirring and the rate of the excitable reaction. In order to clarify and understand the role of the many competing mechanisms present, simplified models of the process are introduced. They are one-dimensional baker-map models for the flow and a one-dimensional approximation for the transverse profile of the filaments.Comment: 14 pages, 16 figure

Coarse-Grained Picture for Controlling Quantum Chaos

We propose a coarse-grained picture to analyze control problems for quantum chaos systems. Using optimal control theory, we first show that almost perfect control is achieved for random matrix systems and a quantum kicked rotor. Second, under the assumption that the controlled dynamics is well described by a Rabi-type oscillaion between unperturbed states, we derive an analytic expression for the optimal field. Finally we numerically confirm that the analytic field can steer an initial state to a target state in random matrix systems.Comment: REVTeX4 with graphicx package, 11 pages, 10 figures; replaced fig.1(a) and 2(a