Stochastic sensitivity of 3D-cycles
Mathematics and Computers in Simulation
Stabilizing Chaos with Predictive Control
Automation and Remote Control
Nonlinear Dynamics of Chaotic and Stochastic Systems: Tutorial and Modern Developments (Springer Series in Synergetics)
Analysis of stochastic attractors under the stationary point-cycle bifurcation
Automation and Remote Control
On control of stochastic sensitivity
Automation and Remote Control
On stochastic sensitivity control in discrete systems
Automation and Remote Control
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For a nonlinear oscillatory stochastic system, we study the control problem for the variance of random trajectories around a deterministic cycle. To describe the range of random trajectories, we use the method of stochastic sensitivity functions. We consider the problem of designing a given stochastic sensitivity function, discuss problems of controllability and reachability. Complete stochastic controllability is only possible when the control's dimension coincides with the system's dimension. Otherwise, the design problem becomes ill-posed. To solve it, we propose a regularization method that lets us produce a given stochastic sensitivity function with any given precision. The efficiency of the proposed approach is demonstrated with the example of controlling stochastic oscillations in a brusselator model.