Stochastic sensitivity analysis of periodic attractors in non-autonomous nonlinear dynamical systems based on stroboscopic map

2014 ◽  
Vol 378 (34) ◽  
pp. 2518-2523 ◽  
Author(s):  
Kong-Ming Guo ◽  
Jun Jiang
Keyword(s):  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical ◽  
Stochastic Sensitivity ◽  
Periodic Attractors ◽  
Stochastic Sensitivity Analysis

scholarly journals Controlling Stochastic Sensitivity by Feedback Regulators in Nonlinear Dynamical Systems with Incomplete Information

Mathematics ◽  
2021 ◽  
Vol 9 (24) ◽  
pp. 3229
Author(s):  
Irina Bashkirtseva
Keyword(s):  
Dynamical Systems ◽  
Incomplete Information ◽  
Matrix Equation ◽  
Nonlinear Dynamical Systems ◽  
Van Der Pol Oscillator ◽  
Nonlinear Dynamical ◽  
Stochastic Sensitivity ◽  
Quadratic Matrix Equation ◽  
Quadratic Matrix ◽  
Stochastic Oscillators

The problem of synthesis of stochastic sensitivity for equilibrium modes in nonlinear randomly forced dynamical systems with incomplete information is considered. We construct a feedback regulator that uses noisy data on some system state coordinates. For parameters of the regulator providing assigned stochastic sensitivity, a quadratic matrix equation is derived. Attainability of the assigned stochastic sensitivity is reduced to the solvability of this equation. We suggest a constructive algorithm for solving this quadratic matrix equation. These general theoretical results are used to solve the problem of stabilizing equilibrium modes of nonlinear stochastic oscillators under conditions of incomplete information. Details of our approach are illustrated on the example of a van der Pol oscillator.

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