Sources of uncertainty in deterministic dynamics: an informal overview

Stewart, Ian

doi:10.1098/rsta.2011.0113

Cited by 13 publications

(5 citation statements)

References 46 publications

(59 reference statements)

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“…The physical world is mostly nonlinear. This is a warning against making assumptions based on traditional linear thinking (Stewart, 2011). To avoid mistakes which stem from phenomenological approach mathematical models have been used.…”

Section: Discussionmentioning

confidence: 99%

A Hybrid Analytical Model of Growth Regulation in Animals

Stass¹

2022

IJB

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The aim of this study was to build and analyse a model of ontogenetic growth of animals. The model was built based on experimental data and field observations. The growth of pigs was modelled by a non-local hybrid technique. This technique treats time as a discrete variable. In this study the growth of pigs was modelled beginning the stage of the rapid growth up to the maximum weight. The growth was modelled as a dynamic system. It was shown that the trajectory of the growth is neither smooth nor continuous. The main theme in this study is transition to a new growth phenotype. There are two results in this study. At a certain point in animal's ontogeny the trajectory of the growth undergoes a first-order phase transition. In the next stage, during bifurcation, new trajectories of growth emerge; this sequence of events has a biological meaning. The emerged trajectories differ from the initial trajectory, and from each other in essence. In the model, one trajectory of the growth emerges instantly. For other growth trajectory to emerge it takes half a year. In a population of animals, it is a general situation. Individual animals can take on only one of the emerged trajectories. In this study, a two-stage process of a transition to a new ontogenetic trajectory or a new phenotype was revealed. The transition to the new growth phenotype is to consider as the model of the pattern of the systemic regulation of growth.

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Section: Discussionmentioning

confidence: 99%

A Hybrid Analytical Model of Growth Regulation in Animals

Stass¹

2022

IJB

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“…The number of phenomena that are amenable to precise analytic description is relatively small. The famous French mathematician Henri Poincaré even proved that the motions of as few as three bodies in mutual gravitational attraction (e.g., sun, moon, and Earth), although governed by exact Newtonian laws, defy an exact solution (e.g., see Stewart, 2011). They can be predicted thousands, but not millions, of years ahead.…”

Section: Theoretical Synthesismentioning

confidence: 99%

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Phaf

2020

Theory & Psychology

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A publication deluge has impeded rather than advanced theory in experimental psychology. Many researchers rely more on null-hypothesis significance testing than literature studies to determine whether results are worthwhile. Four problematic publication practices are symptomatic for the theoretical deficit: (a) reinventing the wheel, (b) the Proteus phenomenon, (c) mechanical (non) replications, and (d) the survival of discredited hypotheses. Remedies include the development of AI tools recommending semantically related references, mandatory hypothesizing before and after results are known, and theoretical syntheses guided by meta-analyses and process models. The nonlinear theoretical development shows parallels to the optimization procedure of biological evolution. Theoretical hypotheses rather than experimental results are the elementary units of science. The fittest theories may survive alongside the least fit because they are not made to compete in research publications. Even if publication practices improve, winning hypotheses will often represent local optima and still cannot be taken with absolute certainty.

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“…The physical world is mostly nonlinear. This observation is the warning to us not to make assumptions based on the traditional linear thinking (Stewart, 2011). In biological systems, interactions and processes are often nonlinear.…”

Section: Nonlinear Processesmentioning

confidence: 99%

“…More specifically, we consider two basic types of dynamic system: discrete, and continuous. In other words, a discrete dynamical system is a difference equation, and a continuous dynamic system is a differential equation, both kinds are deterministic (Stewart, 2011). Hybrid models have been built for systems with a mixture of continuous, and discrete-time dynamic.…”

Section: Hybrid Modelmentioning

confidence: 99%

A Model of Growth Trajectory Bifurcation in Animals Ontogeny

Stass¹

2019

IJB

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The aim of this study was to formulate and analyse a model of ontogenetic growth cessation in pigs. The cessation of growth when an animal reaches its species-specific size in ontogeny is still a problem. Systemic factors that contribute to this process are unknown. The focus of the research is an analysis of the growth dynamic that explains some aspects of the problem.The method applied to meet the purpose of the study was mathematical modelling. To enhance the understanding of the growth trajectory in ontogeny an analytical model of growth in pigs was built. The model was formulated as a hybrid dynamic system with discrete-time, and continuum equations. The novelty of the study is a concept of ontogenetic growth in the pig. Both a new modelling technique, and new variables are introduced. A central theme of the study is an analysis of the growth trajectory bifurcation, and a description of the two emerged growth trajectories. A reading of a normal form of bifurcation applied to the growth trajectory bifurcation has been offered.The results suggest that ontogenetic growth in pigs is not continuous. The growth trajectory has bifurcation at the point the animals attain their individual maximum weight. At this point, two new growth trajectories emerge. On one trajectory, animals continue to grow till a species maximum weight is reached. On other trajectory, animals continue to live till obtainable life span is attained. The emerged trajectories are genetic channels that open the way to grow for the certain phenotypes. Ontogenetic growth stops when the feed conversion coefficient grows into infinity.

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Sources of uncertainty in deterministic dynamics: an informal overview

Cited by 13 publications

References 46 publications

A Hybrid Analytical Model of Growth Regulation in Animals

A Hybrid Analytical Model of Growth Regulation in Animals

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A Model of Growth Trajectory Bifurcation in Animals Ontogeny

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