Complexity in Prosody: A Nonlinear Dynamical Systems Approach for Dyadic Conversations; Behavior and Outcomes in Couples Therapy

2016 ◽  
Author(s):  
Md. Nasir ◽  
Brian Baucom ◽  
Shrikanth S. Narayanan ◽  
Panayiotis Georgiou
Keyword(s):  
Dynamical Systems ◽  
Couples Therapy ◽  
Systems Approach ◽  
Nonlinear Dynamical Systems ◽  
Nonlinear Dynamical

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 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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