Synchronization of solutions of Duffing-type equations with random perturbations

We consider a family of particles with different initial states and/or velocities whose dynamics is described by a Duffing-type equation ẍ+αẋ+P(x)=0 where the velocity v=ẋ is randomly perturbed at random times. We present sufficient conditions ensuring almost identical sample paths of the particl...

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Bibliographic Details
Published in:Nonlinear analysis 2013-12, Vol.93, p.122-131
Main Authors: Ambrazevičius, A., Ivanauskas, F., Mackevičius, V.
Format: Article
Language:English
Subjects:
Density
Duffing-type equation
Intervals
Mathematical analysis
Noise-induced synchronization
Nonlinearity
Perturbation methods
Polynomials
Polypropylenes
Random perturbations
Synchronization
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Summary:We consider a family of particles with different initial states and/or velocities whose dynamics is described by a Duffing-type equation ẍ+αẋ+P(x)=0 where the velocity v=ẋ is randomly perturbed at random times. We present sufficient conditions ensuring almost identical sample paths of the particles after a long time: the times between perturbations are assumed to be unbounded and uniformly positive, and the values of jumps are assumed to be random variables with positive density on a sufficiently large interval [0,H]. The paper generalizes the results of Ambrazevičius et al. (2010)  [11] for P(x)=x3−x to the case of arbitrary higher-order odd polynomials P.
ISSN:0362-546X
1873-5215
DOI:10.1016/j.na.2013.07.031