Confidence tori in the analysis of stochastic 3D-cycles

L. Ryashko, I. Bashkirtseva, A. Gubkin and P. Stikhin

Mathematics and Computers in Simulation (MATCOM), 2009, vol. 80, issue 2, 256-269

Abstract: We present a new computer approach to the spatial analysis of stochastically forced 3D-cycles in nonlinear dynamic systems. This approach is based on a stochastic sensitivity analysis and uses the construction of confidence tori. A confidence torus as a simple 3D-model of the stochastic cycle adequately describes its main probabilistic features. We suggest an effective algorithm for construction of the confidence tori using a discrete set of confidence ellipses. The ability of these tori to visualize thin effects observed for the period-doubling bifurcations zone in the stochastic Roessler model are shown. For this zone, the geometrical growth of stochastic sensitivity of the forced cycles under transition to chaos is presented.

Keywords: Stochastic systems; Cycles; Stochastic sensitivity; Roessler model (search for similar items in EconPapers)
Date: 2009
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Citations: View citations in EconPapers (8)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:matcom:v:80:y:2009:i:2:p:256-269

DOI: 10.1016/j.matcom.2009.06.026

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