Deterministic Chaos Theory: Basic Concepts

Cattani, M.; Caldas, Iberê L.; Souza, Sílvio L.T. de; Iarosz, Kelly C.

doi:10.1590/1806-9126-rbef-2016-0185

Cited by 15 publications

(20 citation statements)

References 24 publications

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“…This small spin in combination with the oiled bowling lane could cause it to move wildly off-course, making it “highly-sensitive” to initial conditions. Due to the effect Poincaré found, “measurements made on the state of a system at a given time may not allow us to predict the future situation” [3] . These systems are now termed “chaotic.” Unpredictability due to highly-sensitive reliance on initial conditions inspired the term “deterministic chaos.” After Poincaré’s studies, the deterministic chaotic behavior was discovered in numerous dynamical systems and confirmed experimentally [2] , [6] , [15] , [20] .…”

Section: Introductionmentioning

confidence: 99%

Is spread of COVID-19 a chaotic epidemic?

Jones

Strigul

2021

Chaos, Solitons & Fractals

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Section: Introductionmentioning

confidence: 99%

Is spread of COVID-19 a chaotic epidemic?

Jones

Strigul

2021

Chaos, Solitons & Fractals

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“…On the basis of plotted images of Poincaré cross-sections [22,23], which were additionally supplemented by analysing the density of point distribution on the phase plane, they were found to exhibit geometrical similarity. This is particularly noticeable with respect to the attractors of D360 and D375 couplings (Fig.…”

Section: Results Of Model Simulationsmentioning

confidence: 99%

Study of flexible couplings non-linear dynamics using bond graphs

Margielewicz

Opasiak

Gąska

et al. 2019

Forsch Ingenieurwes

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The aim of this work is to model the dynamics of flexible couplings. On the basis of a non-linear mathematical model solved by bond graph, the ranges of excitation frequency were determined, in which the movement of the couplings is chaotic. For three couplings, the 3D distributions of the largest Lyapunov exponent and correlation dimension diagram (CDD) were plotted. The proposed diagram (CDD) illustrates how the geometric structure of the attractor changes when the conditions of excitation change. The classic Poincare cross-section, completed by us with the density of points distribution, significantly enhances information about geometrical structures of strange attractors. It has been shown that in relation to large ranges of changes in the control parameter, the geometric structure of the strange attractor is stretched and curved. The areas with the highest densification of the Poincaré cross section are most often located in places where the chaotic attractor is curved. Untersuchung der nichtlinearen Dynamik flexibler Kopplungen mit Hilfe von Bondgraphen ZusammenfassungZiel dieser Arbeit ist es, die Dynamik von elastischen Kupplungen zu modellieren. Anhand eines durch einen Bindungsgraphen gelösten nichtlinearen mathematischen Modells wurden die Bereiche der Anregungsfrequenz bestimmt, in denen die Bewegung der Kopplungen chaotisch ist. Für drei Kopplungen wurden die 3D-Verteilungen des größten Lyapunov-Exponenten und das Korrelationsdimensionsdiagramm (CDD) aufgezeichnet. Das vorgeschlagene Diagramm (CDD) zeigt, wie sich die geometrische Struktur des Attraktors ändert, wenn sich die Anregungsbedingungen ändern. Der von uns vervollständigte klassische Poincaré-Querschnitt mit der Dichte der Punkteverteilung verbessert die Informationen über geometrische Strukturen fremder Attraktoren erheblich. Es hat sich gezeigt, dass in Bezug auf große Änderungsbereiche der Steuerparameter die geometrische Struktur des seltsamen Attraktors gedehnt und gebogen wird. Die Bereiche mit der höchsten Verdichtung des Poincaré-Querschnitts befinden sich am häufigsten an Stellen, an denen der chaotische Attraktor gekrümmt ist.

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“…(4), sua solução pode depender de modo ultrassensível das condições iniciais, caracterizando-os na categoria dos sistemas complexos. Recomenda-se a leitura do artigo de revisão introdutório sobre a teoria do caos determinístico, de Cattani, Caldas e colaboradores [20].…”

Section: Gato E a Borboletáunclassified

Complexidade na Física e seu Ensino: Apresentação da Edição Especial

Studart

2021

Rev. Bras. Ensino Fís.

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Este artigo descreve os 18 artigos e um texto suplementar que compõem a Edição Especial da RBEF sobre a Complexidade na Física e seu Ensino. Nessa edição são abordados temas abrangentes que, de algum modo, contemplam visões diferentes da complexidade por físicos e pesquisadores da ciência da complexidade. Alguns tópicos se enquadram na tradicional física dos sistemas complexos, mas outros extrapolam a área da Física, embora com a atuação de físicos, e são estudados em vários e diferentes campos do conhecimento. São incluídos nessa edição estudos de assuntos complicados, intrincados, que, embora não sejam categorizados como parte da ciência da complexidade, demandam novas abordagens teóricas e métodos experimentais desafiadores. Essa apresentação contém discussões breves do conceito de emergência em contraponto ao de reducionismo, de caos quântico, complexidade na Astrofísica, estudos da mente, física estatística não extensiva, modelos epidemiológicos, migração celular, materiais complexos, escoamentos turbulentos, modelagem computacional, neuroeducação, além da complexidade e dos desafios no Ensino de Física.

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Deterministic Chaos Theory: Basic Concepts

Cited by 15 publications

References 24 publications

Is spread of COVID-19 a chaotic epidemic?

Is spread of COVID-19 a chaotic epidemic?

Study of flexible couplings non-linear dynamics using bond graphs

Complexidade na Física e seu Ensino: Apresentação da Edição Especial

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