Delay Induced Excitability

We analyse the stochastic dynamics of a bistable system under the influence of time-delayed feedback. Assuming an asymmetric potential, we show the existence of a regime in which the systems dynamic displays excitability by calculating the relevant residence time distributions and correlation times. Experimentally we then observe this behaviour in the polarization dynamics of a vertical cavity surface emitting laser with opto-electronic feedback. Extending these observations to two-dimensional systems with dispersive coupling we finally show numerically that delay induced excitability can lead to the appearance of propagating wave-fronts and spirals.Comment: 5 pages, 6 figure

Double coherence resonance in neuron models driven by discrete correlated noise

We study the influence of correlations among discrete stochastic excitatory or inhibitory inputs on the response of the FitzHugh-Nagumo neuron model. For any level of correlation the emitted signal exhibits at some finite noise intensity a maximal degree of regularity, i.e., a coherence resonance. Furthermore, for either inhibitory or excitatory correlated stimuli a {\it Double Coherence Resonance} (DCR) is observable. DCR refers to a (absolute) maximum coherence in the output occurring for an optimal combination of noise variance and correlation. All these effects can be explained by taking advantage of the discrete nature of the correlated inputs.Comment: 4 pages, 3 figures in eps, to appear in Physical Review Letter

Dynamical mechanism of anticipating synchronization in excitable systems

We analyze the phenomenon of anticipating synchronization of two excitable systems with unidirectional delayed coupling which are subject to the same external forcing. We demonstrate for different paradigms of excitable system that, due to the coupling, the excitability threshold for the slave system is always lower than that for the master. As a consequence the two systems respond to a common external forcing with different response times. This allows to explain in a simple way the mechanism behind the phenomenon of anticipating synchronization.Comment: 4 pages including 7 figures. Submitted for publicatio

Control spiral wave dynamics using feedback signals from line detectors

We numerically study trajectories of spiral-wave-cores in excitable systems modulated proportionally to the integral of the activity on the straight line, several or dozens of equi-spaced measuring points on the straight line, the double-line and the contour-line. We show the single-line feedback results in the drift of core center along a straight line being parallel to the detector. An interesting finding is that the drift location in $y$ is a piecewise linear-increasing function of both the feedback line location and time delay. Similar trajectory occurs when replacing the feedback line with several or dozens of equi-spaced measuring points on the straight line. This allows to move the spiral core to the desired location along a chosen direction by measuring several or dozens of points. Under the double-line feedback, the shape of the tip trajectory representing the competition between the first and second feedback lines is determined by the distance of two lines. Various drift attractors in spiral wave controlled by square-shaped contour-line feedback are also investigated. A brief explanation is presented.Comment: 6 pages and 7 figures; Accepted for publication in EPL; Figs.5 and 6 are in JPG forma

Modeling rhythmic patterns in the hippocampus

We investigate different dynamical regimes of neuronal network in the CA3 area of the hippocampus. The proposed neuronal circuit includes two fast- and two slowly-spiking cells which are interconnected by means of dynamical synapses. On the individual level, each neuron is modeled by FitzHugh-Nagumo equations. Three basic rhythmic patterns are observed: gamma-rhythm in which the fast neurons are uniformly spiking, theta-rhythm in which the individual spikes are separated by quiet epochs, and theta/gamma rhythm with repeated patches of spikes. We analyze the influence of asymmetry of synaptic strengths on the synchronization in the network and demonstrate that strong asymmetry reduces the variety of available dynamical states. The model network exhibits multistability; this results in occurrence of hysteresis in dependence on the conductances of individual connections. We show that switching between different rhythmic patterns in the network depends on the degree of synchronization between the slow cells.Comment: 10 pages, 9 figure

Computational inference in systems biology

Parameter inference in mathematical models of biological pathways, expressed as coupled ordinary differential equations (ODEs), is a challenging problem. The computational costs associated with repeatedly solving the ODEs are often high. Aimed at reducing this cost, new concepts using gradient matching have been proposed. This paper combines current adaptive gradient matching approaches, using Gaussian processes, with a parallel tempering scheme, and conducts a comparative evaluation with current methods used for parameter inference in ODEs

Greenhouse gas balance over thaw-freeze cycles in discontinuous zone permafrost

Peat in the discontinuous permafrost zone contains a globally significant reservoir of carbon that has undergone multiple permafrost-thaw cycles since the end of the mid-Holocene (~3700 years before present). Periods of thaw increase C decomposition rates which leads to the release of CO2 and CH4 to the atmosphere creating potential climate feedback. To determine the magnitude and direction of such feedback, we measured CO2 and CH4 emissions and modeled C accumulation rates and radiative fluxes from measurements of two radioactive tracers with differing lifetimes to describe the C balance of the peatland over multiple permafrost-thaw cycles since the initiation of permafrost at the site. At thaw features, the balance between increased primary production and higher CH4 emission stimulated by warmer temperatures and wetter conditions favors C sequestration and enhanced peat accumulation. Flux measurements suggest that frozen plateaus may intermittently (order of years to decades) act as CO2 sources depending on temperature and net ecosystem respiration rates, but modeling results suggest that—despite brief periods of net C loss to the atmosphere at the initiation of thaw—integrated over millennia, these sites have acted as net C sinks via peat accumulation. In greenhouse gas terms, the transition from frozen permafrost to thawed wetland is accompanied by increasing CO2 uptake that is partially offset by increasing CH4 emissions. In the short-term (decadal time scale) the net effect of this transition is likely enhanced warming via increased radiative C emissions, while in the long-term (centuries) net C deposition provides a negative feedback to climate warming

Life History Parameters of Gulf Flounder (Paralichthys albigutta) From Northwest Florida

Age, growth, natural and total mortality, a length-weight relationship, reproductive seasonality, sex ratio, maturity, and reproductive potential by size were estimated for gulf flounder, Paralichthys albigutta, from northwest Florida. The study used a fishery-independent approach during three annual migratory spawning seasons to sample gulf flounder offshore (spearing by divers) and inshore (multipanel trammel nets). We found gulf flounder to be slightly smaller at L∞ than other paralichthids (using either von Bertalanffy or damped growth functions), but gulf flounder obtained larger sizes and older ages than previously thought for this species [females to 575 mm total length (TL) and age 7, males to 373 mm TL and age 11], probably due to offshore sampling targeting more of the adult component of the stock. Given the older age structure than previously noted for this species, gulf flounder maturity and mortality estimates were similar to values reported for other U.S. paralichthids. Gulf flounder exhibited fall-winter gonad development with all evidence pointing to spawning occurring offshore. We estimated batch fecundity and spawning frequency, but it was apparent that there was a seasonal effect for both of these parameters, with increased oocyte density and nearly daily spawning occurring by late October to November, the peak period of development, also reflected in the gonadosomatic index

Distribution, Abundance, and Age Structure of Red Snapper (Lutjanus campechanus) Caught on Research Longlines in U.S. Gulf of Mexico

Two pilot surveys were conducted in the northern Gulf of Mexico (Gulf) to determine the feasibility of sampling red snapper (Lutjanus campechanus) populations in offshore waters with bottom longline gear. The first pilot survey off Mississippi-Alabama was conducted in May 1999 and yielded a total of seven snapper from 60 stations. The second pilot survey was off Texas in June 2000 and yielded a total of 76 snapper from 44 stations. The catch per unit effort was 0.12 red snapper/100 hook hr [coefficient of variation (CV) = 0.54] in 1999 and 1.73 red snapper/100 hook hr (CV = 0.21) in 2000. Otoliths were removed from all collected red snapper, and ages were assigned with an average percent error of 3.71%. Red snapper from the 1999 survey ranged from 405 to 873 mm total length (TL) (545 mm TL median) and from 3 to 19 yr (median age 5 yr). The red snapper from Texas ranged in size from 380 to 903 mm TL (755 mm TL median) and ranged in age from 3 to 53 yr (median age 11 yr). Based on the results of the pilot surveys, expanded longline surveys targeting red snapper were conducted in 2001 and 2002; these surveys yielded 86 snapper and 75 snapper, respectively. The 2001 snapper ranged from 427 to 950 mm TL (770 mm TL median) and from 3 to 37 yr (median age 12 yr). The 2002 snapper ranged from 409 to 950 mm TL (815 mm TL median) and from 4 to 44 yr (median age 13 yr). Twelve red snapper were captured in the eastern Gulf (east of the Mississippi River), and their ages ranged from 3 to 19 yr (median age 6 yr). The 232 red snapper that were caught in the western Gulf ranged in age from 3 to 53 yr (median age 12 yr). A difference in catch rates by depth was also noted with most red snapper captures occurring in the 55-92 m depth range