scholarly journals Spectrum analysis on Fisher-Kolmogorov-Petrovsky-Pischunov equation using Evans function approach

2017 ◽  
Author(s):  
I. I. Lestari ◽  
A. A. Bachtiar ◽  
A. Wibowo
Keyword(s):  
Spectrum Analysis ◽  
Evans Function ◽  
Function Approach

Stability Analysis in Mean-Field Games via an Evans Function Approach

2018 ◽  
Author(s):  
Piyush Grover
Keyword(s):  
Optimal Control ◽  
Stability Analysis ◽  
Mean Field ◽  
Evans Function ◽  
Function Approach ◽  
Mean Field Games ◽  
Mean Field Game ◽  
Large Populations ◽  
Multi Agent ◽  
Hamilton Jacobi Bellman

This work is concerned with stability analysis of stationary and time-varying equilibria in a class of mean-field games that relate to multi-agent control problems of flocking and swarming. The mean-field game framework is a non-cooperative model of distributed optimal control in large populations, and characterizes the optimal control for a representative agent in Nash-equilibrium with the population. A mean-field game model is described by a coupled PDE system of forward-in-time Fokker-Planck (FP) equation for density of agents, and a backward-in-time Hamilton-Jacobi-Bellman (HJB) equation for control. The linear stability analysis of fixed points of these equations typically proceeds via numerical computation of spectrum of the linearized MFG operator. We explore the Evans function approach that provides a geometric alternative to solving the characteristic equation.

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