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

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

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

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

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

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

Thermal Impact on Spiking Properties in Hodgkin-Huxley Neuron with Synaptic Stimulus

The effect of environmental temperature on neuronal spiking behaviors is investigated by numerically simulating the temperature dependence of spiking threshold of the Hodgkin-Huxley neuron subject to synaptic stimulus. We find that the spiking threshold exhibits a global minimum in a "comfortable temperature" range where spike initiation needs weakest synaptic strength, indicating the occurrence of optimal use of synaptic transmission in neural system. We further explore the biophysical origin of this phenomenon in ion channel gating kinetics and also discuss its possible biological relevance in information processing in neural systems.Comment: 10 pages, 4 figure

Limits and dynamics of stochastic neuronal networks with random heterogeneous delays

Realistic networks display heterogeneous transmission delays. We analyze here the limits of large stochastic multi-populations networks with stochastic coupling and random interconnection delays. We show that depending on the nature of the delays distributions, a quenched or averaged propagation of chaos takes place in these networks, and that the network equations converge towards a delayed McKean-Vlasov equation with distributed delays. Our approach is mostly fitted to neuroscience applications. We instantiate in particular a classical neuronal model, the Wilson and Cowan system, and show that the obtained limit equations have Gaussian solutions whose mean and standard deviation satisfy a closed set of coupled delay differential equations in which the distribution of delays and the noise levels appear as parameters. This allows to uncover precisely the effects of noise, delays and coupling on the dynamics of such heterogeneous networks, in particular their role in the emergence of synchronized oscillations. We show in several examples that not only the averaged delay, but also the dispersion, govern the dynamics of such networks.Comment: Corrected misprint (useless stopping time) in proof of Lemma 1 and clarified a regularity hypothesis (remark 1

A propensity criterion for networking in an array of coupled chaotic systems

We examine the mutual synchronization of a one dimensional chain of chaotic identical objects in the presence of a stimulus applied to the first site. We first describe the characteristics of the local elements, and then the process whereby a global nontrivial behaviour emerges. A propensity criterion for networking is introduced, consisting in the coexistence within the attractor of a localized chaotic region, which displays high sensitivity to external stimuli,and an island of stability, which provides a reliable coupling signal to the neighbors in the chain. Based on this criterion we compare homoclinic chaos, recently explored in lasers and conjectured to be typical of a single neuron, with Lorenz chaos.Comment: 4 pages, 3 figure