Large-scale nonlinear dynamical systems: a vector dissipative systems approach

2004 ◽  
Author(s):  
W.M. Haddad ◽  
V.S. Chellaboina ◽  
S.G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Large Scale ◽  
Systems Approach ◽  
Nonlinear Dynamical Systems ◽  
Dissipative Systems ◽  
Nonlinear Dynamical

Large-Scale Impulsive Dynamical Systems

2011 ◽  
Author(s):  
Wassim M. Haddad ◽  
Sergey G. Nersesov
Keyword(s):  
Dynamical Systems ◽  
Lyapunov Functions ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Supply Rate ◽  
Nonlinear Dynamical ◽  
Dissipation Inequality ◽  
Vector Lyapunov Functions ◽  
Definition Of ◽  
Stability Results

This chapter develops vector dissipativity notions for large-scale nonlinear impulsive dynamical systems. In particular, it introduces a generalized definition of dissipativity for large-scale nonlinear impulsive dynamical systems in terms of a hybrid vector dissipation inequality involving a vector hybrid supply rate, a vector storage function, and an essentially nonnegative, semistable dissipation matrix. The chapter also defines generalized notions of a vector available storage and a vector required supply and shows that they are element-by-element ordered, nonnegative, and finite. Extended Kalman-Yakubovich-Popov conditions, in terms of the local impulsive subsystem dynamics and the interconnection constraints, are developed for characterizing vector dissipativeness via vector storage functions for large-scale impulsive dynamical systems. Finally, using the concepts of vector dissipativity and vector storage functions as candidate vector Lyapunov functions, the chapter presents feedback interconnection stability results of large-scale impulsive nonlinear dynamical systems.

Hierarchical Bayesian air conditioning load prediction?A nonlinear dynamical systems approach

2003 ◽  
Vol 34 (11) ◽  
pp. 101-110 ◽  
Author(s):  
Yoshinori Nakajima ◽  
Motoki Saito ◽  
Junjiro Sugi ◽  
Hiroaki Hamagishi ◽  
Takashi Matsumoto
Keyword(s):  
Dynamical Systems ◽  
Air Conditioning ◽  
Systems Approach ◽  
Nonlinear Dynamical Systems ◽  
Hierarchical Bayesian ◽  
Load Prediction ◽  
Nonlinear Dynamical

scholarly journals The Brain Dynamics Toolbox for Matlab

2017 ◽  
Author(s):  
Stewart Heitmann ◽  
Matthew J Aburn ◽  
Michael Breakspear
Keyword(s):  
Dynamical Systems ◽  
Differential Equations ◽  
Computational Neuroscience ◽  
Large Scale ◽  
Nonlinear Dynamical Systems ◽  
Brain Dynamics ◽  
Interactive Simulation ◽  
Nonlinear Dynamical ◽  
Delay Differential ◽  
The Brain

AbstractNonlinear dynamical systems are increasingly informing both theoretical and empirical branches of neuroscience. The Brain Dynamics Toolbox provides an interactive simulation platform for exploring such systems in MATLAB. It supports the major classes of differential equations that arise in computational neuroscience: Ordinary Differential Equations, Delay Differential Equations and Stochastic Differential Equations. The design of the graphical interface fosters intuitive exploration of the dynamics while still supporting scripted parameter explorations and large-scale simulations. Although the toolbox is intended for dynamical models in computational neuroscience, it can be applied to dynamical systems from any domain.

scholarly journals Time-averaging axion-like interacting scalar fields models

2021 ◽  
Vol 81 (11) ◽  
Author(s):  
Saikat Chakraborty ◽  
Esteban González ◽  
Genly Leon ◽  
Bin Wang
Keyword(s):  
Dynamical Systems ◽  
Systems Approach ◽  
Nonlinear Dynamical Systems ◽  
Scalar Fields ◽  
Time Averaging ◽  
Late Time ◽  
Dimensionless Time ◽  
Nonlinear Dynamical ◽  
Time Dynamics ◽  
Klein Gordon

AbstractIn this paper, we study a cosmological model inspired in the axionic matter with two canonical scalar fields $$\phi _1$$ ϕ 1 and $$\phi _2$$ ϕ 2 interacting through a term added to its potential. Introducing novel dynamical variables, and a dimensionless time variable, the resulting dynamical system is studied. The main difficulties arising in the standard dynamical systems approach, where expansion normalized dynamical variables are usually adopted, are due to the oscillations entering the nonlinear system through the Klein–Gordon (KG) equations. This motivates the analysis of the oscillations using methods from the theory of averaging nonlinear dynamical systems. We prove that time-dependent systems, and their corresponding time-averaged versions, have the same late-time dynamics. Then, we study the time-averaged system using standard techniques of dynamical systems. We present numerical simulations as evidence of such behavior.

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