Linear and nonlinear statistical response theories with prototype applications to sensitivity analysis and statistical control of complex turbulent dynamical systems

2019 ◽  
Vol 29 (10) ◽  
pp. 103131 ◽  
Author(s):  
Andrew J. Majda ◽  
Di Qi
Keyword(s):  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Statistical Control ◽  
Linear And Nonlinear

An Efficient Numerical Simulation for Solving Dynamical Systems With Uncertainty

2017 ◽  
Vol 12 (5) ◽  
Author(s):  
Ali Ahmadian ◽  
Soheil Salahshour ◽  
Chee Seng Chan ◽  
Dumitur Baleanu
Keyword(s):  
Dynamical Systems ◽  
Stability And Convergence ◽  
Uncertain Parameters ◽  
Crucial Issue ◽  
Computational Costs ◽  
First Order ◽  
Wide Range ◽  
Linear And Nonlinear ◽  
The Stability ◽  
Fuzzy Dynamical Systems

In a wide range of real-world physical and dynamical systems, precise defining of the uncertain parameters in their mathematical models is a crucial issue. It is well known that the usage of fuzzy differential equations (FDEs) is a way to exhibit these possibilistic uncertainties. In this research, a fast and accurate type of Runge–Kutta (RK) methods is generalized that are for solving first-order fuzzy dynamical systems. An interesting feature of the structure of this technique is that the data from previous steps are exploited that reduce substantially the computational costs. The major novelty of this research is that we provide the conditions of the stability and convergence of the method in the fuzzy area, which significantly completes the previous findings in the literature. The experimental results demonstrate the robustness of our technique by solving linear and nonlinear uncertain dynamical systems.

scholarly journals Some Aspects of Sensitivity Analysis in Variational Data Assimilation for Coupled Dynamical Systems

2015 ◽  
Vol 2015 ◽  
pp. 1-22 ◽  
Author(s):  
Sergei Soldatenko ◽  
Peter Steinle ◽  
Chris Tingwell ◽  
Denis Chichkine
Keyword(s):  
Sensitivity Analysis ◽  
Dynamical Systems ◽  
Data Assimilation ◽  
Weather Prediction ◽  
Computational Cost ◽  
Variational Data Assimilation ◽  
Practical Implementation ◽  
Parameter Uncertainties ◽  
Sensitivity Functions ◽  
Sensitivity Analysis Method

Variational data assimilation (VDA) remains one of the key issues arising in many fields of geosciences including the numerical weather prediction. While the theory of VDA is well established, there are a number of issues with practical implementation that require additional consideration and study. However, the exploration of VDA requires considerable computational resources. For simple enough low-order models, the computational cost is minor and therefore models of this class are used as simple test instruments to emulate more complex systems. In this paper, the sensitivity with respect to variations in the parameters of one of the main components of VDA, the nonlinear forecasting model, is considered. For chaotic atmospheric dynamics, conventional methods of sensitivity analysis provide uninformative results since the envelopes of sensitivity functions grow with time and sensitivity functions themselves demonstrate the oscillating behaviour. The use of sensitivity analysis method, developed on the basis of the theory of shadowing pseudoorbits in dynamical systems, allows us to calculate sensitivity functions correctly. Sensitivity estimates for a simple coupled dynamical system are calculated and presented in the paper. To estimate the influence of model parameter uncertainties on the forecast, the relative error in the energy norm is applied.

scholarly journals On the controllability of fractional dynamical systems

2012 ◽  
Vol 22 (3) ◽  
pp. 523-531 ◽  
Author(s):  
Krishnan Balachandran ◽  
Jayakumar Kokila
Keyword(s):  
Fixed Point ◽  
Dynamical Systems ◽  
Fixed Point Theorem ◽  
Point Theorem ◽  
Matrix Function ◽  
Sufficient Conditions ◽  
Schauder’S Fixed Point Theorem ◽  
Finite Dimensional ◽  
Linear And Nonlinear ◽  
Controllability Grammian

Abstract This paper is concerned with the controllability of linear and nonlinear fractional dynamical systems in finite dimensional spaces. Sufficient conditions for controllability are obtained using Schauder’s fixed point theorem and the controllability Grammian matrix which is defined by the Mittag-Leffler matrix function. Examples are given to illustrate the effectiveness of the theory.

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