Confidence tori in the analysis of stochastic 3D-cycles

✍ Scribed by L. Ryashko; I. Bashkirtseva; A. Gubkin; P. Stikhin

• Publisher: Elsevier Science
• Year: 2009
• Tongue: English
• Weight: 933 KB
• Volume: 80
• Category: Article
• ISSN: 0378-4754
• DOI: 10.1016/j.matcom.2009.06.026

✦ Synopsis

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.