Logistic map
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Study of chaos theory and different maps(Logistic,Lorenz,Circle,Arnold cat maps) and determination of stability by Lypunov exponent.
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Introduction and a historical review
Neural network concepts
Basic models of ANN
Linearly separable functions
Non Linearly separable functions
NN Learning techniques
Associative networks
Mapping networks
Spatiotemporal Network
Stochastic Networks
Chaos Theory & Fractals' Art
The document discusses chaos theory, fractals, and their application in art. It explains that chaos theory studies bringing order to disorder in mathematics and physics. The butterfly effect demonstrates how small changes can lead to large unpredictable consequences. Fractals are never-ending patterns that repeat at increasingly smaller scales found in nature. Benoit Mandelbrot coined the term fractal and drove interest in fractal geometry. The document provides examples of the author's art applying fractal patterns and chaos theory concepts.
On the Dynamics and Synchronization of a Class of Nonlinear High Frequency Ch...
On the Dynamics and Synchronization of a Class of Nonlinear High Frequency Ch...Université de Dschang
M. Kamdoum Tamba Victor a effectué cette présentation dans le cadre de la soutenance publique de sa thèse de Doctorat en Physique, option électronique le 30 mars 2016 dans la salle des conférences de l'Université de Dschang. A l'issue de la défense, le jury présidé par le professeur Paul Woafo lui a décerné la mention Très honorable à l'unanimité de ses membres. Ce jury lui a par ailleurs adressé ses félicitations verbales. Chaos Analysis
This document provides an overview of chaos theory, including:
1) It defines chaos as the apparently noisy, aperiodic behavior in deterministic systems that is sensitive to initial conditions.
2) Important milestones in chaos theory research are discussed, from Poincare in 1890 to fractal geometry work in the 1970s.
3) Attractors, strange attractors, and fractal geometry are introduced as important concepts.
4) Methods for measuring chaos like Lyapunov exponents and entropy are described.
The Chaos Theory ebook FINAL
Project managers face increasing pressures that often result in chaos. They are expected to manage more projects with tighter deadlines and budgets while constantly being accessible. This leads to inefficient collaboration practices and wasted time. While technology aims to help, it also introduces new challenges around communication methods, data security, and version control. Project managers feel overworked and out of their comfort zone as work pressures mount. They report that projects regularly run over budget and timelines slip when they have too many projects. New tools are needed to help project managers work smarter and foster better collaboration.
Maths scert text book model, chapter 7,statistics
This document provides instructions for making frequency tables and histograms from raw data. It discusses how to group raw data into appropriate class intervals for a frequency table. The key steps are counting the frequency of each class, recording the results in a table, and then representing the frequency table graphically as a histogram by drawing rectangles for each class with height proportional to frequency. Examples are given of making frequency tables and histograms from various data sets, including student test scores, temperatures, wages, and heights.
Systems and Chaos Theory
This document discusses systems and chaos theory. It explains that complex adaptive systems like ant colonies, organizations, and markets are made up of interacting agents that self-organize through evolving rules and a dynamic environment. While such systems can exist in states of stasis or chaos with shifting patterns, order can still emerge from their complex and unpredictable behaviors. The document provides sources on chaos theory and systems theory and how they apply to understanding cities, ecosystems, and other complex systems.
Characteristics of complex systems
Although, chaos/complexity theory and SLA have commonplaces, they seem to be different in that chaos/complexity theory offers the wider perspective that has served SLA in the past. As opposed to SLA, chaos/complexity theory encourages linguists to think in relational terms. It refers to the fact that by accepting participation metaphor/language use/emergent grammar position, chaos/complexity theory does not reject psychological perspective. As it is stated , chaos complexity theory like socialists focus on the following issues: 1. all languages are static 2. there are mechanisms for language change 3.language and learning are seen as an open systems.
Nevertheless, C/CT never rejects the following characteristics which psychological perspective focuses on: 1. languages are sensitive to initial conditions 2. there are systemic patterns with dynamic paths.
Chaos Presentation
The document discusses using a symbolic mechanics software called Mechanical Expressions to model chaotic dynamical systems. It defines key terms like dynamical systems and chaos theory. Three main tests are described to identify chaos: the sensitivity test, mixing test, and Fourier transform test. These are applied to a model of a flywheel system to test for chaotic behavior. While useful, the tests each have limitations and no single test can definitively prove a system is chaotic.
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Introduction to Neural networks (under graduate course) Lecture 6 of 9
Introduction to Neural networks (under graduate course) Lecture 6 of 9
Introduction to Neural networks (under graduate course) Lecture 8 of 9
Introduction to Neural networks (under graduate course) Lecture 8 of 9
On the Dynamics and Synchronization of a Class of Nonlinear High Frequency Ch...
On the Dynamics and Synchronization of a Class of Nonlinear High Frequency Ch...
Similar to Logistic map
Strange Attractors
1) The document outlines J.C. Sprott's presentation about modeling chaotic data and strange attractors from an artistic and scientific perspective. 2) Examples of properties of strange attractors are discussed, including fractal structure, non-integer dimension, and sensitivity to initial conditions. Scaling laws for attractor dimension and Lyapunov exponents are also covered. 3) New simple chaotic flows and electrical circuits discovered by Sprott and others are presented as having aesthetic appeal worthy of consideration beyond pure science.
Sacolloq
This document summarizes a physics colloquium presentation about strange attractors in chaotic systems. Strange attractors are fractal patterns that arise in some dynamical systems and are characterized by sensitivity to initial conditions and having a non-integer fractal dimension. The presentation outlines examples of strange attractors like the Lorenz and Hénon attractors. It discusses properties of strange attractors like attractor dimension and Lyapunov exponents. It also shows that chaos is more common at higher dimensions and in neural networks, and evaluates the aesthetic appeal of strange attractors.
Complex Dynamics and Statistics in Hamiltonian 1-D Lattices - Tassos Bountis
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This document provides an outline for a lecture on complex dynamics in Hamiltonian systems. Some key points:
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3) GALI rapidly detects chaos as deviation vectors become aligned, and identifies quasiperiodic motion by vectors remaining independent. It distinguishes weak and strong chaos based on exponential decay rates.Euler lagrange equations of motion mit-holonomic constraints_lecture7
Lagrange's equations provide an alternative method to Newton's laws for deriving the equations of motion for mechanical systems. Lagrange's method uses generalized coordinates and the kinetic and potential energies of the system to derive scalar differential equations, avoiding the need to solve for constraint forces or accelerations directly. The number of degrees of freedom for a system, which determines the number of differential equations needed, depends only on the number of coordinates and constraints and is independent of the particular coordinate system used.
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This document describes OpenLCDFDM, an open-source finite-difference LCD simulator. It summarizes the key components of LCD display structure and models used in the simulator, including the birefringence of liquid crystals, calculation of liquid crystal orientation under electric fields using the Oseen-Frank model, solving the Laplace equation in anisotropic media, and using the extended Jones matrix method for optical calculations. The document also outlines the program structure and demonstrates simulation results for different LCD modes. Future work is proposed to improve the modeling capabilities.
Quantum chaos of generic systems - Marko Robnik
This document summarizes research on quantum chaos, including the principle of uniform semiclassical condensation of Wigner functions, spectral statistics in mixed systems, and dynamical localization of chaotic eigenstates. It discusses how in the semiclassical limit, Wigner functions condense uniformly on classical invariant components. For mixed systems, the spectrum can be seen as a superposition of regular and chaotic level sequences. Localization effects can be observed if the Heisenberg time is shorter than the classical diffusion time. The document presents an analytical formula called BRB that describes the transition between Poisson and random matrix statistics. An example is given of applying this to analyze the level spacing distribution for a billiard system.
Metodo Monte Carlo -Wang Landau
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Introduction to Quantum Monte Carlo
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Hartree fock theory
1. Hartree-Fock theory describes molecules using a linear combination of atomic orbitals to approximate molecular orbitals. It treats electrons as independent particles moving in the average field of other electrons.
2. The Hartree-Fock method involves iteratively solving the Fock equations until self-consistency is reached between the input and output orbitals. This approximates electron correlation by including an average electron-electron repulsion term.
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Characterization of Subsurface Heterogeneity: Integration of Soft and Hard In...
Park, E., Elfeki, A. M. M., Dekking, F.M. (2003). Characterization of subsurface heterogeneity: Integration of soft and hard information using multi-dimensional Coupled Markov chain approach. Underground Injection Science and Technology Symposium, Lawrence Berkeley National Lab., October 22-25, 2003. p.49. Eds. Tsang, Chin.-Fu and Apps, John A.
http://www.lbl.gov/Conferences/UIST/index.html#topics
Computational Motor Control: Kinematics & Dynamics (JAIST summer course)
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Atomic structure
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Nonlinear Optical Materials
This document discusses nonlinear optics and summarizes key topics covered:
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- Applications of nonlinear optics include optical phase conjugation, optical parametric oscillators, optical computing, optical switching, and optical data storage.
Ph 101-9 QUANTUM MACHANICS
The document provides an outline for a course on quantum mechanics. It discusses key topics like the time-dependent Schrodinger equation, eigenvalues and eigenfunctions, boundary conditions for wave functions, and applications like the particle in a box model. Specific solutions to the Schrodinger equation are explored for stationary states with definite energy, including the wave function for a free particle and the quantization of energy for a particle confined to a one-dimensional box.
slides_cedric_weber_1.pdf
This document provides an overview of Cedric Weber's background and research interests, which include dynamical mean field theory (DMFT) and its application to oxide materials. Some key points:
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- He collaborates with theorists and experimentalists on topics like laser
Fundamentals of electromagnetics
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Dsp 2marks
The document outlines the syllabus for a course on digital signal processing. It includes 5 units: 1) Introduction to signals and systems, 2) Discrete time system analysis using z-transforms, 3) Discrete Fourier transforms and computation including fast Fourier transforms, 4) Design of digital filters including FIR and IIR filters, and 5) Digital signal processors and their architecture. It allocates a total of 45 periods to cover these topics. Textbooks recommended for the course provide further information on digital signal processing principles, algorithms, and applications.
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This document provides an introduction to nuclear magnetic resonance (NMR) spectroscopy. It begins with an overview of NMR and spectroscopy. It then reviews common units used in NMR such as time, temperature, magnetic field strength, energy, and frequency. The document consists of introductory chapters that cover topics like the basics of NMR, mathematics relevant to NMR, spin physics, and energy levels. It provides explanations of fundamental NMR concepts such as spin, magnetic moments, energy states, resonance frequency, and relaxation times T1 and T2. The overall document serves as a comprehensive primer on basic NMR principles.
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The document summarizes quantum numbers and selection rules for quantum mechanical systems. It discusses the three quantum numbers - principal (n), orbital angular momentum (l), and magnetic (ml) quantum numbers. Selection rules for transitions between energy levels are determined by calculating oscillating expectation values. Only transitions where the quantum numbers change by specific values (e.g. l changes by ±1) are allowed. The document also discusses how angular momentum is quantized in quantum mechanics and relates to the quantum numbers l and ml.
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Knowledge of cause-effect relationships is central to the field of climate science, supporting mechanistic understanding, observational sampling strategies, experimental design, model development and model prediction. While the major causal connections in our planet's climate system are already known, there is still potential for new discoveries in some areas. The purpose of this talk is to make this community familiar with a variety of available tools to discover potential cause-effect relationships from observed or simulation data. Some of these tools are already in use in climate science, others are just emerging in recent years. None of them are miracle solutions, but many can provide important pieces of information to climate scientists. An important way to use such methods is to generate cause-effect hypotheses that climate experts can then study further. In this talk we will (1) introduce key concepts important for causal analysis; (2) discuss some methods based on the concepts of Granger causality and Pearl causality; (3) point out some strengths and limitations of these approaches; and (4) illustrate such methods using a few real-world examples from climate science.Similar to Logistic map (20)
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Deep Software Variability and Frictionless Reproducibility
Deep Software Variability and Frictionless ReproducibilityUniversity of Rennes, INSA Rennes, Inria/IRISA, CNRS
The ability to recreate computational results with minimal effort and actionable metrics provides a solid foundation for scientific research and software development. When people can replicate an analysis at the touch of a button using open-source software, open data, and methods to assess and compare proposals, it significantly eases verification of results, engagement with a diverse range of contributors, and progress. However, we have yet to fully achieve this; there are still many sociotechnical frictions.
Inspired by David Donoho's vision, this talk aims to revisit the three crucial pillars of frictionless reproducibility (data sharing, code sharing, and competitive challenges) with the perspective of deep software variability.
Our observation is that multiple layers — hardware, operating systems, third-party libraries, software versions, input data, compile-time options, and parameters — are subject to variability that exacerbates frictions but is also essential for achieving robust, generalizable results and fostering innovation. I will first review the literature, providing evidence of how the complex variability interactions across these layers affect qualitative and quantitative software properties, thereby complicating the reproduction and replication of scientific studies in various fields.
I will then present some software engineering and AI techniques that can support the strategic exploration of variability spaces. These include the use of abstractions and models (e.g., feature models), sampling strategies (e.g., uniform, random), cost-effective measurements (e.g., incremental build of software configurations), and dimensionality reduction methods (e.g., transfer learning, feature selection, software debloating).
I will finally argue that deep variability is both the problem and solution of frictionless reproducibility, calling the software science community to develop new methods and tools to manage variability and foster reproducibility in software systems.
Exposé invité Journées Nationales du GDR GPL 2024
Thornton ESPP slides UK WW Network 4_6_24.pdf
ESPP presentation to EU Waste Water Network, 4th June 2024 “EU policies driving nutrient removal and recycling
and the revised UWWTD (Urban Waste Water Treatment Directive)”
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Plant breeding for disease resistance is a strategy to reduce crop losses caused by disease. Plants have an innate immune system that allows them to recognize pathogens and provide resistance. However, breeding for long-lasting resistance often involves combining multiple resistance genes
Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
The pygmy halfbeak Dermogenys colletei, is known for its viviparous nature, this presents an intriguing case of relatively low fecundity, raising questions about potential compensatory reproductive strategies employed by this species. Our study delves into the examination of fecundity and the Gonadosomatic Index (GSI) in the Pygmy Halfbeak, D. colletei (Meisner, 2001), an intriguing viviparous fish indigenous to Sarawak, Borneo. We hypothesize that the Pygmy halfbeak, D. colletei, may exhibit unique reproductive adaptations to offset its low fecundity, thus enhancing its survival and fitness. To address this, we conducted a comprehensive study utilizing 28 mature female specimens of D. colletei, carefully measuring fecundity and GSI to shed light on the reproductive adaptations of this species. Our findings reveal that D. colletei indeed exhibits low fecundity, with a mean of 16.76 ± 2.01, and a mean GSI of 12.83 ± 1.27, providing crucial insights into the reproductive mechanisms at play in this species. These results underscore the existence of unique reproductive strategies in D. colletei, enabling its adaptation and persistence in Borneo's diverse aquatic ecosystems, and call for further ecological research to elucidate these mechanisms. This study lends to a better understanding of viviparous fish in Borneo and contributes to the broader field of aquatic ecology, enhancing our knowledge of species adaptations to unique ecological challenges.
8.Isolation of pure cultures and preservation of cultures.pdf
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如何办理(uvic毕业证书)维多利亚大学毕业证本科学位证书原版一模一样
原版纸张【微信：741003700 】【(uvic毕业证书)维多利亚大学毕业证】【微信：741003700 】学位证，留信认证（真实可查，永久存档）offer、雅思、外壳等材料/诚信可靠,可直接看成品样本，帮您解决无法毕业带来的各种难题！外壳，原版制作，诚信可靠，可直接看成品样本。行业标杆！精益求精，诚心合作，真诚制作！多年品质 ,按需精细制作，24小时接单,全套进口原装设备。十五年致力于帮助留学生解决难题，包您满意。
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Equivariant neural networks and representation theory
Or: Beyond linear.
Abstract: Equivariant neural networks are neural networks that incorporate symmetries. The nonlinear activation functions in these networks result in interesting nonlinear equivariant maps between simple representations, and motivate the key player of this talk: piecewise linear representation theory.
Disclaimer: No one is perfect, so please mind that there might be mistakes and typos.
dtubbenhauer@gmail.com
Corrected slides: dtubbenhauer.com/talks.html
Bob Reedy - Nitrate in Texas Groundwater.pdf
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THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...
THEMATIC APPERCEPTION TEST(TAT) cognitive abilities, creativity, and critic...Abdul Wali Khan University Mardan,kP,Pakistan
hematic appreciation test is a psychological assessment tool used to measure an individual's appreciation and understanding of specific themes or topics. This test helps to evaluate an individual's ability to connect different ideas and concepts within a given theme, as well as their overall comprehension and interpretation skills. The results of the test can provide valuable insights into an individual's cognitive abilities, creativity, and critical thinking skills20240520 Planning a Circuit Simulator in JavaScript.pptx
Evaporation step counter work. I have done a physical experiment.
(Work in progress.)
Deep Behavioral Phenotyping in Systems Neuroscience for Functional Atlasing a...
Functional Magnetic Resonance Imaging (fMRI) provides means to characterize brain activations in response to behavior. However, cognitive neuroscience has been limited to group-level effects referring to the performance of specific tasks. To obtain the functional profile of elementary cognitive mechanisms, the combination of brain responses to many tasks is required. Yet, to date, both structural atlases and parcellation-based activations do not fully account for cognitive function and still present several limitations. Further, they do not adapt overall to individual characteristics. In this talk, I will give an account of deep-behavioral phenotyping strategies, namely data-driven methods in large task-fMRI datasets, to optimize functional brain-data collection and improve inference of effects-of-interest related to mental processes. Key to this approach is the employment of fast multi-functional paradigms rich on features that can be well parametrized and, consequently, facilitate the creation of psycho-physiological constructs to be modelled with imaging data. Particular emphasis will be given to music stimuli when studying high-order cognitive mechanisms, due to their ecological nature and quality to enable complex behavior compounded by discrete entities. I will also discuss how deep-behavioral phenotyping and individualized models applied to neuroimaging data can better account for the subject-specific organization of domain-general cognitive systems in the human brain. Finally, the accumulation of functional brain signatures brings the possibility to clarify relationships among tasks and create a univocal link between brain systems and mental functions through: (1) the development of ontologies proposing an organization of cognitive processes; and (2) brain-network taxonomies describing functional specialization. To this end, tools to improve commensurability in cognitive science are necessary, such as public repositories, ontology-based platforms and automated meta-analysis tools. I will thus discuss some brain-atlasing resources currently under development, and their applicability in cognitive as well as clinical neuroscience.
EWOCS-I: The catalog of X-ray sources in Westerlund 1 from the Extended Weste...
Context. With a mass exceeding several 104 M⊙ and a rich and dense population of massive stars, supermassive young star clusters
represent the most massive star-forming environment that is dominated by the feedback from massive stars and gravitational interactions
among stars.
Aims. In this paper we present the Extended Westerlund 1 and 2 Open Clusters Survey (EWOCS) project, which aims to investigate
the influence of the starburst environment on the formation of stars and planets, and on the evolution of both low and high mass stars.
The primary targets of this project are Westerlund 1 and 2, the closest supermassive star clusters to the Sun.
Methods. The project is based primarily on recent observations conducted with the Chandra and JWST observatories. Specifically,
the Chandra survey of Westerlund 1 consists of 36 new ACIS-I observations, nearly co-pointed, for a total exposure time of 1 Msec.
Additionally, we included 8 archival Chandra/ACIS-S observations. This paper presents the resulting catalog of X-ray sources within
and around Westerlund 1. Sources were detected by combining various existing methods, and photon extraction and source validation
were carried out using the ACIS-Extract software.
Results. The EWOCS X-ray catalog comprises 5963 validated sources out of the 9420 initially provided to ACIS-Extract, reaching a
photon flux threshold of approximately 2 × 10−8 photons cm−2
s
−1
. The X-ray sources exhibit a highly concentrated spatial distribution,
with 1075 sources located within the central 1 arcmin. We have successfully detected X-ray emissions from 126 out of the 166 known
massive stars of the cluster, and we have collected over 71 000 photons from the magnetar CXO J164710.20-455217.
ESR spectroscopy in liquid food and beverages.pptx
With increasing population, people need to rely on packaged food stuffs. Packaging of food materials requires the preservation of food. There are various methods for the treatment of food to preserve them and irradiation treatment of food is one of them. It is the most common and the most harmless method for the food preservation as it does not alter the necessary micronutrients of food materials. Although irradiated food doesn’t cause any harm to the human health but still the quality assessment of food is required to provide consumers with necessary information about the food. ESR spectroscopy is the most sophisticated way to investigate the quality of the food and the free radicals induced during the processing of the food. ESR spin trapping technique is useful for the detection of highly unstable radicals in the food. The antioxidant capability of liquid food and beverages in mainly performed by spin trapping technique.
The use of Nauplii and metanauplii artemia in aquaculture (brine shrimp).pptx
Although Artemia has been known to man for centuries, its use as a food for the culture of larval organisms apparently began only in the 1930s, when several investigators found that it made an excellent food for newly hatched fish larvae (Litvinenko et al., 2023). As aquaculture developed in the 1960s and ‘70s, the use of Artemia also became more widespread, due both to its convenience and to its nutritional value for larval organisms (Arenas-Pardo et al., 2024). The fact that Artemia dormant cysts can be stored for long periods in cans, and then used as an off-the-shelf food requiring only 24 h of incubation makes them the most convenient, least labor-intensive, live food available for aquaculture (Sorgeloos & Roubach, 2021). The nutritional value of Artemia, especially for marine organisms, is not constant, but varies both geographically and temporally. During the last decade, however, both the causes of Artemia nutritional variability and methods to improve poorquality Artemia have been identified (Loufi et al., 2024).
Brine shrimp (Artemia spp.) are used in marine aquaculture worldwide. Annually, more than 2,000 metric tons of dry cysts are used for cultivation of fish, crustacean, and shellfish larva. Brine shrimp are important to aquaculture because newly hatched brine shrimp nauplii (larvae) provide a food source for many fish fry (Mozanzadeh et al., 2021). Culture and harvesting of brine shrimp eggs represents another aspect of the aquaculture industry. Nauplii and metanauplii of Artemia, commonly known as brine shrimp, play a crucial role in aquaculture due to their nutritional value and suitability as live feed for many aquatic species, particularly in larval stages (Sorgeloos & Roubach, 2021).
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Deep Software Variability and Frictionless Reproducibility
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mô tả các thí nghiệm về đánh giá tác động dòng khí hóa sau đốt
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Unlocking the mysteries of reproduction: Exploring fecundity and gonadosomati...
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aziz sancar nobel prize winner: from mardin to nobel
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8.Isolation of pure cultures and preservation of cultures.pdf
8.Isolation of pure cultures and preservation of cultures.pdf
Equivariant neural networks and representation theory
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20240520 Planning a Circuit Simulator in JavaScript.pptx
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ESR spectroscopy in liquid food and beverages.pptx
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Logistic map
- 1. Chaos theory and Logistic maps Summer Project Report Narendra Kumar Supervisor: Prof. Srikanth Sastry
- 2. Future Plan: Topological Entropy : Quantify chaos ➢ Calculation of Topological entropy for higher dimensional map ➢ Calculation of topological entropy in spin-glass
- 3. Q.Why and how we study non-linear dynamics? Ans. Most of the systems are non-linear in nature. A theoretical study of such a system leads to the solution of nonlinear differential equation. we can extract a lot of informations about solution from the equation themselves. If the dynamical systems be autonomous systems then it can be decomposed Into coupled first order differential equations and then can be solved computationally. Chaos: Its main features are : ➢ extreme sensitivity to initial conditions ➢ Non-linearity ➢ strangeness “Edward Lorenz” described chaos as “when the present determines the future, but the approximate present doesn't approximately determines the future”.
- 4. Lyapunov Exponent: Sensitivity to initial conditions and parameters of a non-linear system is determined by the value of Lyapunov exponent. n λ = lim (1/n) ∑ |df(xi )/dx| n→∞ i=0 If λ (<>0) then orbit is stable, unstable(show chaos). Arnold Transform: a n×n pixel size 2D image and transform each point (x,y) by transformation equation Γ : (x,y) → (x+y,x+2y) mod n after a finite no. of iteration(say k) same image is restored. But there is no any specific relation between k & n.
- 5. RESULTS: (1) Logistic function map:
- 10. (4) Circle map: θ(t+1) = θ(t)+Ω+(K/2π) sin(2πθ(t)) mod1 0<θ(t)<=1 Lyapunov constant graph
- 11. Applications: (1)weather prediction (2)population growth (3)cardiotocography (4) signal analysis (5) random number generator (6) Information theory (7) optics References: (1)Periodic entrainment of chaotic logistic map dynamics:E. Atlee Jackson, Alfred Hübler (2)Lyapunov graph for two-parameters map: Application to the circle map by Figueiredo (3)Deterministic Non-periodic flow: Edward N. Lorenz (4)Nonlinear dynamics and chaos (Book) : Strogatz (5) Arnold cat map : Gabriel Peterson
- 12. THANK YOU