scholarly journals Padé-Type Model Reduction of Second-Order and Higher-Order Linear Dynamical Systems

2005 ◽  
pp. 191-223 ◽  
Author(s):  
Roland W. Freund
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Higher Order ◽  
Second Order ◽  
Type Model ◽  
Linear Dynamical Systems ◽  
Order Linear

scholarly journals $\mathcal{H}_2$ Model Reduction for Large-Scale Linear Dynamical Systems

2008 ◽  
Vol 30 (2) ◽  
pp. 609-638 ◽  
Author(s):  
S. Gugercin ◽  
A. C. Antoulas ◽  
C. Beattie
Keyword(s):  
Dynamical Systems ◽  
Model Reduction ◽  
Large Scale ◽  
Linear Dynamical Systems

scholarly journals Second-Order Model Reduction Based on Gramians

2012 ◽  
Vol 2012 ◽  
pp. 1-9 ◽  
Author(s):  
Cong Teng
Keyword(s):  
Model Order Reduction ◽  
Large Scale ◽  
Order Reduction ◽  
Second Order ◽  
Balanced Truncation ◽  
Order Model ◽  
Model Order ◽  
Linear Dynamical Systems ◽  
Large Scale Systems ◽  
Order Linear

Some new and simple Gramian-based model order reduction algorithms are presented on second-order linear dynamical systems, namely, SVD methods. Compared to existing Gramian-based algorithms, that is, balanced truncation methods, they are competitive and more favorable for large-scale systems. Numerical examples show the validity of the algorithms. Error bounds on error systems are discussed. Some observations are given on structures of Gramians of second order linear systems.

scholarly journals Qualitative features of a NPZ-Model.

BIOMATH ◽  
2021 ◽  
Vol 10 (1) ◽  
pp. 2101067
Author(s):  
Yaya Youssouf Yaya ◽  
Diene Ngom ◽  
Mamadou Sy
Keyword(s):  
Dynamical Systems ◽  
Qualitative Study ◽  
Limit Cycle ◽  
Higher Order ◽  
Stability Of Solutions ◽  
Linear Dynamical Systems ◽  
Internal Equilibrium ◽  
Non Linear

Qualitative study of higher order non linear dynamical systems? is a rewarding experience and a great challenge. This reflective paper is an attempt to deeply analyze interaction features between nutrients, phytoplanktons and zooplanktons by building a so-called NPZ-Model. We used classical methods (of Lyapunov, Hopf, etc.) to examine existence, positivity, boundedness and stability of solutions. Our main contribution is the implementation of a meaningful space parameter that simultaneously guarantees instability of equilibria at the border and? stability of the internal equilibrium. In the case of internal equilibrium instability, we observed the emergence of limit cycle which means the existence of periodical solutions.

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