Noise-induced dynamics in bistable systems with delay

Noise-induced dynamics of a prototypical bistable system with delayed feedback is studied theoretically and numerically. For small noise and magnitude of the feedback, the problem is reduced to the analysis of the two-state model with transition rates depending on the earlier state of the system. In this two-state approximation, we found analytical formulae for the autocorrelation function, the power spectrum, and the linear response to a periodic perturbation. They show very good agreement with direct numerical simulations of the original Langevin equation. The power spectrum has a pronounced peak at the frequency corresponding to the inverse delay time, whose amplitude has a maximum at a certain noise level, thus demonstrating coherence resonance. The linear response to the external periodic force also has maxima at the frequencies corresponding to the inverse delay time and its harmonics.Comment: 4 pages, 4 figures, submitted to Physical Review Letter

Stochastic Resonance in Nonpotential Systems

We propose a method to analytically show the possibility for the appearance of a maximum in the signal-to-noise ratio in nonpotential systems. We apply our results to the FitzHugh-Nagumo model under a periodic external forcing, showing that the model exhibits stochastic resonance. The procedure that we follow is based on the reduction to a one-dimensional dynamics in the adiabatic limit, and in the topology of the phase space of the systems under study. Its application to other nonpotential systems is also discussed.Comment: Submitted to Phys. Rev.

Statistical-Mechanical Measure of Stochastic Spiking Coherence in A Population of Inhibitory Subthreshold Neurons

By varying the noise intensity, we study stochastic spiking coherence (i.e., collective coherence between noise-induced neural spikings) in an inhibitory population of subthreshold neurons (which cannot fire spontaneously without noise). This stochastic spiking coherence may be well visualized in the raster plot of neural spikes. For a coherent case, partially-occupied "stripes" (composed of spikes and indicating collective coherence) are formed in the raster plot. This partial occupation occurs due to "stochastic spike skipping" which is well shown in the multi-peaked interspike interval histogram. The main purpose of our work is to quantitatively measure the degree of stochastic spiking coherence seen in the raster plot. We introduce a new spike-based coherence measure $M_s$ by considering the occupation pattern and the pacing pattern of spikes in the stripes. In particular, the pacing degree between spikes is determined in a statistical-mechanical way by quantifying the average contribution of (microscopic) individual spikes to the (macroscopic) ensemble-averaged global potential. This "statistical-mechanical" measure $M_s$ is in contrast to the conventional measures such as the "thermodynamic" order parameter (which concerns the time-averaged fluctuations of the macroscopic global potential), the "microscopic" correlation-based measure (based on the cross-correlation between the microscopic individual potentials), and the measures of precise spike timing (based on the peri-stimulus time histogram). In terms of $M_s$, we quantitatively characterize the stochastic spiking coherence, and find that $M_s$ reflects the degree of collective spiking coherence seen in the raster plot very well. Hence, the "statistical-mechanical" spike-based measure $M_s$ may be used usefully to quantify the degree of stochastic spiking coherence in a statistical-mechanical way.Comment: 16 pages, 5 figures, to appear in the J. Comput. Neurosc

Dynamical mean-field theory of spiking neuron ensembles: response to a single spike with independent noises

Dynamics of an ensemble of $N$-unit FitzHugh-Nagumo (FN) neurons subject to white noises has been studied by using a semi-analytical dynamical mean-field (DMF) theory in which the original $2 N$-dimensional {\it stochastic} differential equations are replaced by 8-dimensional {\it deterministic} differential equations expressed in terms of moments of local and global variables. Our DMF theory, which assumes weak noises and the Gaussian distribution of state variables, goes beyond weak couplings among constituent neurons. By using the expression for the firing probability due to an applied single spike, we have discussed effects of noises, synaptic couplings and the size of the ensemble on the spike timing precision, which is shown to be improved by increasing the size of the neuron ensemble, even when there are no couplings among neurons. When the coupling is introduced, neurons in ensembles respond to an input spike with a partial synchronization. DMF theory is extended to a large cluster which can be divided into multiple sub-clusters according to their functions. A model calculation has shown that when the noise intensity is moderate, the spike propagation with a fairly precise timing is possible among noisy sub-clusters with feed-forward couplings, as in the synfire chain. Results calculated by our DMF theory are nicely compared to those obtained by direct simulations. A comparison of DMF theory with the conventional moment method is also discussed.Comment: 29 pages, 2 figures; augmented the text and added Appendice

Stepping Stones: A Leadership Development Program to Inspire and Promote Reflection Among Women Faculty and Staff

Women frequently benefit from focused faculty development opportunities not because they need to be “fixed,” but rather it is a means to demonstrate that success, even in chilly environments, is possible. The Stepping Stones program uses a unique design to provide participants with inspiration, time for reflection, and strategies for how to navigate one's career, through hearing about the journeys of successful women. In this article, we describe the program and evaluation results. Post‐event and longitudinal follow‐up surveys indicate that the program and its unique narrative format help to debunk the superwoman myth and leave participants with a sense of optimism about their future careers

Absolute and convective instabilities of parallel propagating circularly polarized Alfvén waves: numerical results

Context.The stability of parallel propagating circularly polarized Alfvén waves (pump waves) has been studied for more than four decades with the use of normal mode analysis. It is well known that the normal mode analysis does not answer the question if a pump wave looks stable or unstable in a particular reference frame. To answer this question it is necessary to find out if the instability is absolute or convective in this reference frame. Aims.We extend our previous study of absolute and convective instabilities of pump waves with small amplitude to pump waves with arbitrary amplitude. Methods.To study the absolute and convective instabilities of pump waves with arbitrary amplitude we numerically implement Brigg's method. Results.We show that the wave is absolutely unstable in a reference frame moving with the velocity U with respect to the rest plasma if U satisfies the inequality Ul Ur) we study the signalling problem. We show that spatially amplifying waves exist only when the signalling frequency is in two symmetric frequency bands, and calculate the dependences of the boundaries of these bands on U for different values of a . We also obtain the dependences of the maximum spatial amplification rate on U for different values of a . The implication of these results on the interpretation of observational data from space missions is discussed. In particular, it is shown that circularly polarized Alfvén waves propagating in the solar wind are convectively unstable in a reference frame of any realistic spacecraft

Stochastic Resonance in Noisy Non-Dynamical Systems

We have analyzed the effects of the addition of external noise to non-dynamical systems displaying intrinsic noise, and established general conditions under which stochastic resonance appears. The criterion we have found may be applied to a wide class of non-dynamical systems, covering situations of different nature. Some particular examples are discussed in detail.Comment: 4 pages, RevTex, 3 PostScript figures available upon reques

Autonomous stochastic resonance in fully frustrated Josephson-junction ladders

We investigate autonomous stochastic resonance in fully frustrated Josephson-junction ladders, which are driven by uniform constant currents. At zero temperature large currents induce oscillations between the two ground states, while for small currents the lattice potential forces the system to remain in one of the two states. At finite temperatures, on the other hand, oscillations between the two states develop even below the critical current; the signal-to-noise ratio is found to display array-enhanced stochastic resonance. It is suggested that such behavior may be observed experimentally through the measurement of the staggered voltage.Comment: 6 pages, 11 figures, to be published in Phys. Rev.

Stochastic Resonance in a Dipole

We show that the dipole, a system usually proposed to model relaxation phenomena, exhibits a maximum in the signal-to-noise ratio at a non-zero noise level, thus indicating the appearance of stochastic resonance. The phenomenon occurs in two different situations, i.e. when the minimum of the potential of the dipole remains fixed in time and when it switches periodically between two equilibrium points. We have also found that the signal-to-noise ratio has a maximum for a certain value of the amplitude of the oscillating field.Comment: 4 pages, RevTex, 6 PostScript figures available upon request; to appear in Phys. Rev.

Parametric instabilities in magnetized multicomponent plasmas

This paper investigates the excitation of various natural modes in a magnetized bi-ion or dusty plasma. The excitation is provided by parametrically pumping the magnetic field. Here two ion-like species are allowed to be fully mobile. This generalizes our previous work where the second heavy species was taken to be stationary. Their collection of charge from the background neutral plasma modifies the dispersion properties of the pump and excited waves. The introduction of an extra mobile species adds extra modes to both these types of waves. We firstly investigate the pump wave in detail, in the case where the background magnetic field is perpendicular to the direction of propagation of the pump wave. Then we derive the dispersion equation relating the pump to the excited wave for modes propagating parallel to the background magnetic field. It is found that there are a total of twelve resonant interactions allowed, whose various growth rates are calculated and discussed.Comment: Published in May 2004; this is a late submission to the archive. 14 pages, 8 figure