The concept of force in population dynamics

Hayward, John; Roach, Paul A.

doi:10.1016/j.physa.2019.121736

Cited by 6 publications

(13 citation statements)

References 41 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…The system stabilises because

B_{1}

is more powerful than

R_{1}

, as it has the greater influence on the energy of the system and, therefore, on the rate of change of the stocks. This result supports Hayward and Roach's (2019) assertion that oscillations are best understood by averaging over one cycle. It also demonstrates the explanatory value of cumulative measures as, although power is an instantaneous measure, average power over the cycle is an accumulation, the work done divided by the period.…”

Section: Energy and Higher Order Feedbacksupporting

confidence: 88%

“…This pattern confirms Sterman's informal description that the balancing loops are gaining in strength , cited earlier (Sterman, 2000, p. 123). Although the loop impacts have successfully explained the curvature in stock behaviour—an instantaneous view—they have not completely explained why both stocks collapse to zero, as the same impact dominance pattern occurs with recovery and oscillation when, for example, the natural death rate of deer is increased (Ford, 2010; Hayward and Roach, 2019; Meadows, 2008). The collapse is not a consequence of an effect that happens in an instant, but an accumulation of effects over the cycle.…”

Section: Overshoot and Collapsementioning

confidence: 99%

“…The underline subscripts indicate the causal pathway, reading from left to right. The impact measures the curvature of stock behaviour over time, dimensions

T^{- 1}

, such that a constant impact results in exponential stock behaviour (Hayward and Roach, 2019). As this model only has a single force, the impact

I_{\underline{italicyx}}

is responsible for the whole of the acceleration of

x

.…”

Section: The Concept Of Energy In a Stock–flow Systemmentioning

confidence: 99%

See 2 more Smart Citations

The concept of energy in the analysis of system dynamics models

Hayward

Roach

2022

System Dynamics Review

Self Cite

View full text Add to dashboard Cite

This paper applies for the first time the Newtonian concept of energy to stock-flow systems and employs it to relate system behaviour to model structure. Kinetic energy and work done are defined analytically using the concepts of loop impact and force from the Newtonian Interpretative Framework and are examined numerically within system dynamics simulations. The energy analogy is used to analyse models by understanding how loops of different orders and types act as energy sources, sinks and exchange, using the system dynamics equivalent of the workenergy theorem. It is shown that energy describes the cumulative effects of feedback on stock behaviour, in contrast to the instantaneous description given by existing methods of loop dominance. This approach gives additional insight over that of existing dominance methods, capturing the dynamical influence of loops even when not dominant. The analogy's explanatory power provides quantitative and informal analysis.

show abstract

“…The system stabilises because

B_{1}

is more powerful than

R_{1}

Section: Energy and Higher Order Feedbacksupporting

confidence: 88%

Section: Overshoot and Collapsementioning

confidence: 99%

“…The underline subscripts indicate the causal pathway, reading from left to right. The impact measures the curvature of stock behaviour over time, dimensions

T^{- 1}

, such that a constant impact results in exponential stock behaviour (Hayward and Roach, 2019). As this model only has a single force, the impact

I_{\underline{italicyx}}

is responsible for the whole of the acceleration of

x

.…”

Section: The Concept Of Energy In a Stock–flow Systemmentioning

confidence: 99%

See 1 more Smart Citation

The concept of energy in the analysis of system dynamics models

Hayward

Roach

2022

System Dynamics Review

Self Cite

View full text Add to dashboard Cite

show abstract

“…Specifically, new methods are available and implemented in standard system dynamics modeling software for analyzing the influence of feedback mechanisms on the dynamic behavior of systems in terms dominant feedback loops (for an overview of this development, see Ford, 1999 ; Hayward & Boswell, 2014 ; Hayward & Roach, 2019 ; Oliva, 2016 ; Richardson, 1995 ; Sato, 2016 ; and Schoenberg et al, 2020 ). In particular, the recent developments implemented in isee Systems Stella Architect ( 2020 ) using loop scores (Schoenberg et al, 2020 ) provide a computationally efficient way to analyze and visualize feedback systems in terms of the relative contribution of each feedback loop on the overall dynamics of a system.…”

Section: Introductionmentioning

confidence: 99%

System Dynamics of Cognitive Vulnerabilities and Family Support Among Latina Children and Adolescents

Hovmand

Calzada

Gulbas

et al. 2022

Clin Child Fam Psychol Rev

View full text Add to dashboard Cite

The paper describes an approach to developing a data-driven development of a feedback theory of cognitive vulnerabilities and family support focused on understanding the dynamics experienced among Latina children, adolescents, and families. Family support is understood to be a response to avoidant and maladaptive behaviors that may be characteristic of cognitive vulnerabilities commonly associated depression and suicidal ideation. A formal feedback theory is developed, appraised, and analyzed using a combination of secondary analysis of qualitative interviews (N = 30) and quantitative analysis using system dynamics modeling and simulation. Implications for prevention practice, treatment, and future research are discussed.

show abstract

“…The model has one reinforcing loop driving the growth and two balancing loops in opposition. Loop impacts are computed numerically using Hayward & Boswell's (2014) method and confirmed analytically using pathway differentiation (Hayward & Roach, 2017;2019). There is no need to consider average loop impact here as there is only one stock in each loop.…”

Section: Limits-to-growth Modelmentioning

confidence: 99%

The Concept of Average Loop Impact as a System-Wide Measure of Feedback Dominance Analysis

Hayward

2020

Preprint

Self Cite

View full text Add to dashboard Cite

In system dynamics, the concept of loop impact measures the effect of a feedback loop on the curvature in the behaviour of the stocks in the loop (Hayward & Boswell, 2014). It is a ratio measure of the acceleration imparted by the loop into a stock and can also be thought of as a ratio measure of the force exerted between adjacent stocks in the loop (Hayward & Roach, 2017). As such, a loop of n stocks is described by n impacts. Loop impact is used to examine regions of loop dominance in stock behaviour. Sometimes, it is helpful to present a dominance analysis for a complete system rather than an individual stock. This paper introduces the concept of average loop impact to explore such a systemwide loop dominance analysis.

show abstract

The concept of force in population dynamics

Cited by 6 publications

References 41 publications

The concept of energy in the analysis of system dynamics models

The concept of energy in the analysis of system dynamics models

System Dynamics of Cognitive Vulnerabilities and Family Support Among Latina Children and Adolescents

The Concept of Average Loop Impact as a System-Wide Measure of Feedback Dominance Analysis

Contact Info

Product

Resources

About