Qualitative Upper and Lower Approximations of Complex Nonlinear Chaotic and Nonchaotic Models

Kód výsledku v IS VaVaI

<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216305%3A26510%2F16%3APU117183" target="_blank" >RIV/00216305:26510/16:PU117183 - isvavai.cz</a>

Výsledek na webu

<a href="http://www.worldscientific.com/doi/10.1142/S0218127415501734" target="_blank" >http://www.worldscientific.com/doi/10.1142/S0218127415501734</a>

DOI - Digital Object Identifier

<a href="http://dx.doi.org/10.1142/S0218127415501734" target="_blank" >10.1142/S0218127415501734</a>

Jazyk výsledku

angličtina

Název v původním jazyce

Qualitative Upper and Lower Approximations of Complex Nonlinear Chaotic and Nonchaotic Models

Popis výsledku v původním jazyce

Soft sciences, e.g. economics, ecology, sociology and their various integrations, are often used to develop e.g. forecasting models and optimization constraints. However, highly nonlinear, vague, partially inconsistent and multidimensional systems are prohibitively difficult to study at the quantitative level. Different types of quantitative simplifications are therefore used, e.g. linearization. The resulting models are oversimplified and therefore inapplicable results are often obtained. There are just three values used to quantify qualitative variables and their derivatives: plus/increasing; zero/constant; negative/decreasing. It means that a set of scenarios, i.e. the qualitative solution, is discrete. A qualitative model can be simplified by ignoring some of its equations. The simplified model is less restrictive and gives more scenarios. This set of scenarios is the model’s upper approximation. An additional equation makes the model more complex and the resulting set of fewer scenarios is the lower approximation. A qualitative model of dumped oscillations, upper and lower approximations of well-known Lorenz model and a vaguely known five-dimensional bankruptcy model are presented in detail. The upper approximation of the Lorenz set of differential equations has 213 and its lower approximation has 189 scenarios. No a prioriknowledge of qualitative models theory is required.

Název v anglickém jazyce

Qualitative Upper and Lower Approximations of Complex Nonlinear Chaotic and Nonchaotic Models

Popis výsledku anglicky

Soft sciences, e.g. economics, ecology, sociology and their various integrations, are often used to develop e.g. forecasting models and optimization constraints. However, highly nonlinear, vague, partially inconsistent and multidimensional systems are prohibitively difficult to study at the quantitative level. Different types of quantitative simplifications are therefore used, e.g. linearization. The resulting models are oversimplified and therefore inapplicable results are often obtained. There are just three values used to quantify qualitative variables and their derivatives: plus/increasing; zero/constant; negative/decreasing. It means that a set of scenarios, i.e. the qualitative solution, is discrete. A qualitative model can be simplified by ignoring some of its equations. The simplified model is less restrictive and gives more scenarios. This set of scenarios is the model’s upper approximation. An additional equation makes the model more complex and the resulting set of fewer scenarios is the lower approximation. A qualitative model of dumped oscillations, upper and lower approximations of well-known Lorenz model and a vaguely known five-dimensional bankruptcy model are presented in detail. The upper approximation of the Lorenz set of differential equations has 213 and its lower approximation has 189 scenarios. No a prioriknowledge of qualitative models theory is required.

Druh

J_imp - Článek v periodiku v databázi Web of Science

CEP obor

—

OECD FORD obor

10101 - Pure mathematics

Projekt

—

Návaznosti

S - Specificky vyzkum na vysokych skolach

Rok uplatnění

2016

Kód důvěrnosti údajů

S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

Název periodika

International Journal of Bifurcations & Chaos

ISSN

0218-1274

e-ISSN

1793-6551

Svazek periodika

25

Číslo periodika v rámci svazku

13

Stát vydavatele periodika

SG - Singapurská republika

Počet stran výsledku

12

Strana od-do

1-12

Kód UT WoS článku

000367751100005

EID výsledku v databázi Scopus

2-s2.0-84954304491