Stochastic bifurcations, chaos and phantom attractors in the Langford system with tori. (English) Zbl 1460.37050
Summary: The variability of stochastic dynamics for a three-dimensional dynamic model in a parametric zone with 2-tori is investigated. It is shown how weak Gaussian noise transforms deterministic quasiperiodic oscillations into noisy bursting. The phenomenon of stochastic generation of a phantom attractor and its shift with noise amplification is revealed. This phenomenon, accompanied by order-chaos transitions, is studied in terms of stochastic \(P\)- and \(D\)-bifurcations.
MSC:
| 37H20 | Bifurcation theory for random and stochastic dynamical systems |
| 60H10 | Stochastic ordinary differential equations (aspects of stochastic analysis) |
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