scholarly journals Linear Stability Analysis of Multiparameter Dynamical Systems via a Numerical-Perturbation Approach

AIAA Journal ◽  
2011 ◽  
Vol 49 (9) ◽  
pp. 2047-2056 ◽  
Author(s):  
Angelo Luongo ◽  
Francesco D'Annibale
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Perturbation Approach

Dynamical systems on networks

2018 ◽  
Author(s):  
Mark Newman
Keyword(s):  
Stability Analysis ◽  
Dynamical Systems ◽  
Systems Theory ◽  
Linear Stability ◽  
Linear Stability Analysis ◽  
Limit Cycles ◽  
Spectral Properties ◽  
Stability Conditions ◽  
Short Introduction ◽  
The Stability

An introduction to the theory of dynamical systems on networks. This chapter starts with a short introduction to classical (non-network) dynamical systems theory, including linear stability analysis, fixed points, and limit cycles. Dynamical systems on networks are introduced, focusing initially on systems with only one variable per node and progressing to multi-variable systems. Linear stability analysis is developed in detail, leading to master stability conditions and the connection between stability and the spectral properties of networks. The chapter ends with a discussion of synchronization phenomena, the stability of limit cycles, and master stability conditions for synchronization.

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