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Monday, April 20, 2020 | History

12 edition of The Logistic Map and the Route to Chaos found in the catalog.

The Logistic Map and the Route to Chaos

From the Beginnings to Modern Applications (Understanding Complex Systems)

by

  • 194 Want to read
  • 24 Currently reading

Published by Springer .
Written in English

    Subjects:
  • Numerical analysis,
  • Physics,
  • Mathematics,
  • Science,
  • Science/Mathematics,
  • Applied,
  • Science / Physics,
  • Verhulst,
  • logistic map,
  • population dynamics,
  • (Pierre Franðcois),,
  • 1804-1849,
  • Chaotic behavior in systems,
  • Verhulst, P.-F

  • Edition Notes

    ContributionsMarcel Ausloos (Editor), Michel Dirickx (Editor)
    The Physical Object
    FormatHardcover
    Number of Pages413
    ID Numbers
    Open LibraryOL9055842M
    ISBN 103540283668
    ISBN 109783540283669


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The Logistic Map and the Route to Chaos Download PDF EPUB FB2

Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of.

Route to Chaos in Generalized Logistic Map Article (PDF Available) in Acta Physica Polonica Series a (3a) February with Reads How we measure 'reads'. Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics, physics, chemistry, biology, economics and sociology.

Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. Get this from a library. The logistic map and the route to chaos: from the beginnings to modern applications.

[M Ausloos; M Dirickx;] -- Pierre-Francois Verhulst, with his seminal work using the logistic map to describe population growth and saturation, paved the way for the many applications of this tool in modern mathematics.

Indeed nowadays the logistic map is considered a useful and paradigmatic showcase for the route leading to chaos. This volume gathers contributions from some of the leading specialists in the field to present a state-of-the art view of the many ramifications of Format: Paperback.

The logistic map, period-doubling and universal constants The period-doubling route to chaos has been observed in many different contexts (chemical reactions, electronic circuits, dripping taps - at least in theory,) and the same universal constant d found in the book by nning,‘Stability, Instability and Chaos’).File Size: 91KB.

ISBN: OCLC Number: Description: xx, pages: illustrations ; 24 cm: Contents: Chaotic growth with the logistic model of P.-F. Verhulst / H. Pastijn --Pierre-François Verhulst's final triumph / J.

Kint, D. Constales, A. Vanderbauwhede --Limits to iron law of Verhulst / P.L. Kunsch --Recurrent generation of Verhulst chaos maps The Logistic Map and the Route to Chaos book any order and.

Intermittency route to chaos in the Logistic Map. Intermittency and intermittency routes to chaos in logistic Map: The phenomenon of Intermittency is a routeto chaos in nonlinear systems. THE-MAP-OF-CHAOS Download The-map-of-chaos ebook PDF or Read Online books in PDF, EPUB, and Mobi Format.

Click Download or Read Online button to THE-MAP-OF-CHAOS book pdf for free now. The Map Of Chaos. Author: Félix J. Palma ISBN: The Logistic Map And The Route To Chaos. Author: Marcel Ausloos ISBN: Genre.

These are videos from the Introduction to Complexity course hosted on Complexity Explorer. You will learn about the tools used by scientists to. Marcel Ausloos is the author of The Logistic Map and the Route to Chaos ( avg rating, 1 rating, 0 reviews, published ), Magnetic Phase Transition 3/5(1).

The Logistic Map and the Route to Chaos: From The Beginnings to Modern Applications, Understanding Complex SystemsCited by: Chaos associated with bifurcation makes a new science, but the origin and essence of chaos are not yet clear.

Based on the well-known logistic map, chaos used to be regarded as intrinsic randomicity of determinate dynamics systems. However, urbanization dynamics indicates new explanation about it.

Using mathematical derivation, numerical computation, and empirical analysis, we can explore Author: Yanguang Chen. The Intermittency Route to Chaos. Prof. Schuster. Christian Albrecht University Kiel, Department of Theoretical Physics, Germany United Kingdom.

Search for more papers by this author. Book Author(s): Prof. Schuster. Christian Albrecht University Kiel, Department of Theoretical Physics, Germany.

Search for more papers by. An example is the bifurcation diagram of the logistic map: + = (−). The bifurcation parameter r is shown on the horizontal axis of the plot and the vertical axis shows the set of values of the logistic function visited asymptotically from almost all initial conditions.

The bifurcation diagram shows the forking of the periods of stable orbits from 1 to 2 to 4 to 8 etc. The route to chaos of the coupled logistic map is studied. We observe a flip bifurcation from a stable fixed point to a stable period-2 orbit which is followed by a Hopf bifurcation, quasiperiodic behaviour and periodic orbits.

At the end of the route the iteration scheme tends to a fascinating strange attractor looking like the Eiffel by: 1. Abstract Citations (1) References Recurrent Generation of Verhulst Chaos Maps at Any Order and Their Stabilization Diagram by Anticipative Control Dubois, Daniel M.

Abstract. Publication: The Logistic Map and the Route to Chaos: From The Beginnings to Modern Applications, Understanding Complex Systems. Pub Date: DOI: / Title: Chaos and the Logistic Map 1 Chaos and the Logistic Map.

PHYS ; by Lesa Moore ; DEPARTMENT OF PHYSICS ; 2 Different Types of Growth 3 (No Transcript) 4 (No Transcript) 5 (No Transcript) 6 A Population Example. Every generation, the population of fish in a lake grows by Nn is the population of generation n. r is the. Preface. Introduction.

Fractals: A cantor set. The Koch triadic island. Fractal dimensions. The logistic map: The linear map. The fixed points and their stability. Period two. The period doubling route to chaos. Feigenbaum's constants. Chaos and strange attractors. The critical point and its iterates.

Self similarity, scaling and univerality. Dynamical systems described by iterated map functions are used to explore the period-doubling route to chaos, Lyapunov exponents, and Feigenbaum numbers.

A simple derivation of the numerical value of the Feigenbaum number α is provided. The connections among differential equation models, Poincare sections, and iterated maps are explored.

This chapter explores the logistic map, the sine map. logistic map, are given. The dynamical system is obtained by iterating the function f(x) = ax(l - x), where a is a fixed parameter in the interval [0,4]. Let xo be an initial point in the interval [0,1]; note that then all future values of the system also lie in [0,1].

To get a bit of the flavor of this map, exampleFile Size: 2MB. The logistic map is a discrete-time demographic model analogous to the continuous-time logistic equation [3] and is a simple example of how chaotic behavior can arise.

In this chapter we are mainly interested in linear systems, since there exist many well established analysis tools. The Quadratic Map Program for the Apple Macintosh computer allows the user to easily run, analyze, see, and hear data from the quadratic map (aka, the logistic map): which is the simplest example of a nonlinear system exhibiting chaotic and complex behavior.

Like it’s cousin, the bouncing ball program, the quadratic map program strictly follows the Macintosh interface guidelines. The finding of “chaos” along the way of a period-doubling route or other routes, therefore is just more confirmation that the logistic map or equation contains an inherent complexity playing itself out as the complex systems modeled by it evolve, change, adapt, grow, die, and so forth.

Chaos and Time-Series Analysis J. Sprott A web page supplement to the book by the above title. This page contains supplementary materials, computer software, color figures, animations, errata, and links to web resources for the text Chaos and Time-Series Analysis (Oxford University Press, ).It is organized according to the chapters in the book.

The phase plane is introduced to discuss nonlinear phenomena. Discrete models for population growth are also presented, and when teaching in recent years I have supplemented the book with a discussion of iterations of the logistic map and the period doubling route to chaos.

Abstract Pierre-François Verhulst was born years ago. After a short biography of P.-F. Verhulst in which the link with the Royal Military Academy in Brussels is emphasized, the early history of the so-called "Logistic Model" is described. In the previous post on chaos theory we looked at the logistic map, a simple 1-D discrete map which illustrates chaotic behaviour.

This map was defined by the following equation. We’re going to be looking at the maps dependence upon the parameter value r. The logistic map shows a wide range of different behaviours depending upon our choice of r.

Chapter 2. Bifurcation and the Logistic Family The basin of attraction The logistic family Periodic Points Periodic points of the logistic map The period doubling route to chaos The bifurcation diagram for the logistic map and the occurrence of period 3.

The tent family The 2-cycles of the tent family Chapter 3. The logistic map is an extremely simple equation and is completely deterministic: every xt maps onto one and only one value of xt+1.

And yet the chaotic trajectories obtained from this map, at certain values of R, look very random—enough so that the logistic map has been used as a basis for generating pseudo-random numbers on a computer.

and periodic points. Towards the end of the chapter, the period-doubling route to chaos is presented. In particular, the logistic map is given in detail, including its fixed points, 2 and 4-periodic cycles.

The chapter ends with a presentation of 2 fish population models as an application of the above concepts. The complete bifurcation diagram of the logistic map is barely mentioned in the well-known chaos textbooks.

Yet, in a few researches, it was briefly discussed (Ambadan and Joseph,Bresten and Jung,Gutiérrez and Iglesias,Shimada et al.,Tsuchiya and Yamagishi, ) with the claim of having no real-world Cited by: 1. Recurrent Generation of Verhulst Chaos Maps at Any Order and Their Stabilization Diagram by Anticipative Control: Authors: Dubois, Daniel M.

Affiliation: AA(Institute of Mathematics, asbl CHAOS, Centre for Hyperincursion and Anticipation in Ordered Systems) Publication: The Logistic Map and the Route to Chaos, Understanding Complex Systems. The logistic map features such universal features on route to chaos that we expect they must occur in Nature.

Nobel prize winning work on phase transitions now being applied to the onset of chaos and transitions to chaos. Logistic map has no scientific content, no laws of nature, PURE numerology. 2d Logistic Map Matlab Code. For these values of r, the logistic map becomes very sensitive to the initial value of x, displaying thus a basic characteristic of chaotic behavior.

Such a route to chaos is called a “period doubling scenario” and the resulting graph, highly reminiscent of Klee’s strata, is. The Logistic Map and the Route to Chaos: From The Beginnings to Modern Applications Springer-Verlag Berlin Heidelberg Hugo Pastijn (auth.), Professor Dr.

Marcel Ausloos, Dr. Michel Dirickx (eds.). On chaos he covers, among other topics, iterated functions, discrete dynamical systems and the logistic function, sensitive dependence to initial conditions, Lyapunov exponents, the shadowing lemma, bifurcation diagrams and the universality of the period-doubling route to chaos, and renormalization.

properties of chaotic systems. We first make a brief introduction to chaos in general and then we show some important properties of chaotic systems using the logistic map and its bifurcation diagram. We also show the universality found in “the route to chaos”.

The user is only required to have notions of algebra, so it is quite accessible. The Logistic Map and the Route to Chaos.

From The Beginnings to Modern Applications This title is included in the Springer Complexity program Series: Understanding Complex SystemsApprox. p., Hardcover ISBN: About this book. Kint, Jos, Denis Constales, and André Vanderbauwhede. “Pierre-François Verhulst’s Final Triumph.” In The Logistic Map and the Route to Chaos: Understanding Complex Systems, ed.

Marcel Ausloos and Michel Dirickx, 13–Dordrecht, The Netherlands: Springer.Kellert’s () focus on chaos models is suggestive of the semantic view of theories, and many texts and articles on chaos focus on models (e.g., logistic map, Henon map, Lorenz attractor). Briefly, on the semantic view, a theory is characterized by (1) some set of models and (2) the hypotheses linking these models with idealized physical.In this recipe, we will simulate a famous chaotic system: the logistic map.

This is an archetypal example of how chaos can arise from a very simple nonlinear equation. The logistic map models the evolution of a population, taking into account both reproduction and density-dependent mortality (starvation).