Nonlinear Dynamics of Group Dynamics: Models from Mathematical Sociology

Three Kinds of Gear Transmission Nonlinear Dynamics Models

Advanced Materials Research ◽

10.4028/www.scientific.net/amr.787.765 ◽

2013 ◽

Vol 787 ◽

pp. 765-770

Author(s):

Li Juan Wu ◽

Jin Yuan Tang ◽

Si Yu Chen

Keyword(s):

Nonlinear Dynamics ◽

Numerical Simulation ◽

Time Domain ◽

Rotation Angle ◽

Dynamic Responses ◽

Relative Rotation ◽

Dissipation Energy ◽

Motion Equations ◽

Low Speed ◽

Dynamics Models

Based on the Lagranges equations, a new nonlinear dynamic gear model is established by introducing two variables of relative rotation angleand mean rotation angle. The motion equations derived with Lagranges equation exhibit nonlinear terms which are absent in the equations derived on Newtons equations. Combining with the numerical simulation, the dynamic responses in time domain and frequency domain are deduced, and it can be concluded that the responses at low speed of three different models are different. However, they are similar at the designed speed without the consideration of dissipation energy. On the contrary, the dynamic responses are similar at low speed and the simplified Newtons equation differs at the designed speed including dissipation energy.

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Strong and weak nonlinear dynamics: Models, classification, examples

Acoustical Physics ◽

10.1134/s1063771013060171 ◽

2013 ◽

Vol 59 (6) ◽

pp. 644-650 ◽

Cited By ~ 11

Author(s):

O. V. Rudenko ◽

C. M. Hedberg

Keyword(s):

Nonlinear Dynamics ◽

Dynamics Models

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Modelling Consensus Emergence With Nonlinear Dynamics

10.31234/osf.io/n4gfc ◽

2022 ◽

Author(s):

Yvette Baurne ◽

Frédéric Delmar ◽

Jonas Wallin

Keyword(s):

Nonlinear Dynamics ◽

Group Dynamics ◽

Work Group ◽

Dynamic Interactions ◽

Data Set ◽

Group Research ◽

Invariant Statistic ◽

The Individual ◽

Time Form ◽

Over Time

The study of emergent, bottom-up, processes has long been of interest within organizational and group research. Emergent processes refer to how dynamic interactions among lower-level units (e.g. individuals) over time form a new, shared, construct or phenomena at a higher level (e.g. work group). To properly study emergence of shared constructs one needs models, and data, that both take into account variability across individuals and groups (multilevel), and variability over time (longitudinal). This article makes three contribution to the modelling and theory of of consensus emergence. First, we formulate two separate patterns of consensus emergence; homogeneous and heterogeneous. Homogeneous consensus emergence is characterized by gradual and almost deterministic adjustments of the individual trajectories, whereas heterogeneous consensus emergence show more randomly oscillating trajectories towards consensus. Second, we introduce a model-invariant statistic that measures the strength of the consensus; and allows for comparisons between different models and patterns of consensus emergence. Third, we show how Gaussian Processes can be used to further extend the consensus emergence models, allowing them to capture nonlinear dynamics, on both individual and group level, in emergent processes. Using an established data set, we show that conclusions on the pattern of consensus emergence can change depending on whether the nonlinear group mean change over time is adequately modelled or not. Thus it is crucial to correctly capture the group dynamics to properly understand the consensus emergence.

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Nonlinear Modeling by Interpolation Between Linear Dynamics and Its Application in Control

Journal of Dynamic Systems Measurement and Control ◽

10.1115/1.2789473 ◽

2007 ◽

Vol 129 (6) ◽

pp. 813-824 ◽

Cited By ~ 8

Author(s):

Kiriakos Kiriakidis

Keyword(s):

Nonlinear Dynamics ◽

Linear Growth ◽

Linear Models ◽

Nonlinear Modeling ◽

Approximation Error ◽

Basis Functions ◽

Linear Matrix ◽

Matrix Inequalities ◽

Growth Bound ◽

Dynamics Models

This paper proposes a finite series expansion to approximate general nonlinear dynamics models to arbitrary accuracy. The method produces an approximation of nonlinear dynamics in the form of an aggregate of linear models, weighted by unimodal basis functions, and results in a linear growth bound on the approximation error. Furthermore, this paper demonstrates that the proposed approximation satisfies the modeling assumptions for analysis based on linear matrix inequalities and hence widens the applicability of these techniques to the area of nonlinear control.

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