Noise-induced synchronization and anti-resonance in excitable systems; Implications for information processing in Parkinson's Disease and Deep Brain Stimulation

We study the statistical physics of a surprising phenomenon arising in large networks of excitable elements in response to noise: while at low noise, solutions remain in the vicinity of the resting state and large-noise solutions show asynchronous activity, the network displays orderly, perfectly synchronized periodic responses at intermediate level of noise. We show that this phenomenon is fundamentally stochastic and collective in nature. Indeed, for noise and coupling within specific ranges, an asymmetry in the transition rates between a resting and an excited regime progressively builds up, leading to an increase in the fraction of excited neurons eventually triggering a chain reaction associated with a macroscopic synchronized excursion and a collective return to rest where this process starts afresh, thus yielding the observed periodic synchronized oscillations. We further uncover a novel anti-resonance phenomenon: noise-induced synchronized oscillations disappear when the system is driven by periodic stimulation with frequency within a specific range. In that anti-resonance regime, the system is optimal for measures of information capacity. This observation provides a new hypothesis accounting for the efficiency of Deep Brain Stimulation therapies in Parkinson's disease, a neurodegenerative disease characterized by an increased synchronization of brain motor circuits. We further discuss the universality of these phenomena in the class of stochastic networks of excitable elements with confining coupling, and illustrate this universality by analyzing various classical models of neuronal networks. Altogether, these results uncover some universal mechanisms supporting a regularizing impact of noise in excitable systems, reveal a novel anti-resonance phenomenon in these systems, and propose a new hypothesis for the efficiency of high-frequency stimulation in Parkinson's disease

Entrainment in forced Winfree systems

Rhythmic behavior is widely present in living organisms. The rhythms can be innate and usually they are externally stimulated by the environment. One such stimulus is the 24 h natural light-dark cycle which governs the activity-inactivity cycle of many plants, animals and humans. The cells in the suprachiasmatic nucleus that govern our circadian rhythms are ideally regarded as a group of biological oscillators. In the Winfree model, the biological oscillators are regarded as coupled oscillators. The Winfree model was used to describe the synchronization of a large system of globally coupled phase oscillators. Considering that external stimuli and environmental factors, such as the change of light and darkness, have great influence on the rhythmic behavior, a periodic forcing is added to Winfree system. The thesis focuses on a case where the mean natural frequency of the oscillators is the same with the frequency of the external forcing. A simple case is analyzed with the Poincare map for only one forced oscillator. Then through a careful study of synchronized states and stability on identical oscillators, we obtain the entrainment degree. For a more general case, we study the state diagrams of non-identical oscillators whose natural frequencies follow a uniform or a Lorentz distribution. The Ott-Antonsen is used to give a low-dimensional dynamical description of the system. Then we study the case of detuned systems. We investigate the difference between the detuned and non-detuned cases for identical oscillators and understand the entrainment patterns using stability theory

Dynamical Effects of Nuclear Rings in Disk Galaxies

We investigate the dynamical response of stellar orbits in a rotating barred galaxy potential to the perturbation by a nuclear gaseous ring. The change in 3D periodic orbit families is examined as the gas accumulates between the inner Lindblad resonances. It is found that the phase space allowable to the x2 family of orbits is substantially increased and a vertical instability strip appears with the growing mass of the ring. A significant distortion of the x1 orbits is observed in the vicinity of the ring, which leads to the intersection between orbits with different values of the Jacobi integral. We also examine the dependence of the orbital response to the eccentricity and alignment of the ring with the bar. Misalignment between an oval ring and a bar can leave observational footprints in the form of twisted near-infrared isophotes in the vicinity of the ring. It is inferred that a massive nuclear ring acts to weaken and dissolve the stellar bar exterior to the ring, whereas only weakly affecting the orbits interior to the inner Lindblad resonances. Consequences for gas evolution in the circumnuclear regions of barred galaxies are discussed as well.Comment: 27 pages, 11 postscript figures included, latex using aastex 4.0, uuencoded compressed tar file, to appear in Ap

Dynamics of Barred Galaxies

Some 30% of disc galaxies have a pronounced central bar feature in the disc plane and many more have weaker features of a similar kind. Kinematic data indicate that the bar constitutes a major non-axisymmetric component of the mass distribution and that the bar pattern tumbles rapidly about the axis normal to the disc plane. The observed motions are consistent with material within the bar streaming along highly elongated orbits aligned with the rotating major axis. A barred galaxy may also contain a spheroidal bulge at its centre, spirals in the outer disc and, less commonly, other features such as a ring or lens. Mild asymmetries in both the light and kinematics are quite common. We review the main problems presented by these complicated dynamical systems and summarize the effort so far made towards their solution, emphasizing results which appear secure. (Truncated)Comment: This old review appeared in 1993. Plain tex with macro file. 82 pages 18 figures. A pdf version with figures at full resolution (3.24MB) is available at http://www.physics.rutgers.edu/~sellwood/bar_review.pd