30,991 research outputs found
Multi-condition of stability for nonlinear stochastic non-autonomous delay differential equation
A nonlinear stochastic differential equation with the order of nonlinearity
higher than one, with several discrete and distributed delays and time varying
coefficients is considered. It is shown that the sufficient conditions for
exponential mean square stability of the linear part of the considered
nonlinear equation also are sufficient conditions for stability in probability
of the initial nonlinear equation. Some new sufficient condition of stability
in probability for the zero solution of the considered nonlinear non-autonomous
stochastic differential equation is obtained which can be considered as a
multi-condition of stability because it allows to get for one considered
equation at once several different complementary of each other sufficient
stability conditions. The obtained results are illustrated with numerical
simulations and figures.Comment: Published at https://doi.org/10.15559/18-VMSTA110 in the Modern
Stochastics: Theory and Applications (https://www.i-journals.org/vtxpp/VMSTA)
by VTeX (http://www.vtex.lt/
Characteristics of in-out intermittency in delay-coupled FitzHugh-Nagumo oscillators
We analyze a pair of delay-coupled FitzHugh-Nagumo oscillators exhibiting
in-out intermittency as a part of the generating mechanism of extreme events.
We study in detail the characteristics of in-out intermittency and identify the
invariant subsets involved --- a saddle fixed point and a saddle periodic orbit
--- neither of which are chaotic as in the previously reported cases of in-out
intermittency. Based on the analysis of a periodic attractor possessing in-out
dynamics, we can characterize the approach to the invariant synchronization
manifold and the spiralling out to the saddle periodic orbit with subsequent
ejection from the manifold. Due to the striking similarities, this analysis of
in-out dynamics explains also in-out intermittency.Comment: 15 pages, 6 figure
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