[Show abstract][Hide abstract] ABSTRACT: The minimal two-dimensional model of bursting neuronal dynamics is used to study the influence of time-delay on the properties of synchronization of bursting neurons. Generic properties of bursting and dependence of the stability of synchronization on the time-lag and the strength of coupling are described, and compared with the two common types of synaptical coupling, i.e., time-delayed chemical and electrical synapses.
Chinese Physics B 01/2012; 21(1). · 1.15 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Influence of small time-delays in coupling between noisy excitable systems on the coherence resonance and self-induced stochastic
resonance is studied. Parameters of delayed coupled deterministic excitable units are chosen such that the system has only
one attractor, namely the stationary state, for any value of the coupling and the time-lag. Addition of white noise induces
qualitatively different types of coherent oscillations, and we analyzed the influence of coupling time-delay on the properties
of these coherent oscillations. The main conclusion is that time-lag τ≥1, but still smaller than the refractory period, and sufficiently strong coupling drastically change signal to noise ratio
in the quantitative and qualitative way. An interval of noise values implies quite large signal to noise ratio and different
types of noise induced coherence are greatly enhanced. We also observed coincident spiking for small noise intensity and time-lag
proportional to the inter-spike interval of the coherent spike trains. On the other hand, time-lags τ<1 and/or weak coupling induce negligible changes in the properties of the stochastic coherence.
Journal of Statistical Physics 01/2011; 145(1):175-186. · 1.40 Impact Factor
[Show abstract][Hide abstract] ABSTRACT: Two delayed coupled excitable systems with internal delays are studied. For different parametric values each of the isolated units displays excitable, bi-stable or oscillatory dynamics. Bifurcational relations among coupling time-lag and coupling constant for different values of the internal time-lags are obtained. Possible types of synchronization between the units in typical dynamical regimes are studied.
[Show abstract][Hide abstract] ABSTRACT: Excitable and oscillatory dynamics of delayed locally coupled type I and type II excitable systems is analyzed. Diffusive and sigmoid coupling have been considered. It is shown that the stability and the patterns of exactly synchronous oscillations depend on the type of excitability and the type of coupling. However, within the same class, characterized by the excitability type and the coupling the dynamics qualitatively depends only on whether the number of units is even or odd.
[Show abstract][Hide abstract] ABSTRACT: Bifurcations and typical dynamics of an in-homogeneous chain of excitable systems with delayed coupling are compared with the corresponding homogeneous system, recently studied in the Ref. [Phys. Rev. E 67 (2003) 066222]. It is shown that the typical features of the long term dynamics are robust with respect to small random in-homogeneity in the parameters. However, some atypical features related to more complicated bifurcations of the stationary solution could be different.