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Theory and applications of nonlinear dynamics and chaos

Theory and applications of nonlinear dynamics and chaos
A tantárgyleírás hatályossága
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Subject name (Hungarian, English)
Theory and applications of nonlinear dynamics and chaos
Theory and applications of nonlinear dynamics and chaos
Subject code BMEVIMMD307
Subject type —
Training Level —
Course types and hours (weekly/semester)
Course type lecture tutorial laboratory
hours (weekly) 4 0 0
type (linked/independent) — — —
Assessment type vizsga
Credits 5
Subject coordinator
Dr. Kolumbán Géza
position: egyetemi docens
Responsible department
—
Faculty
Subject website http://www.mit.bme.hu/oktatas/targyak/vimmd307/
Primary curriculum type —
Direct prerequisites – Strong prerequisite none
Direct prerequisites – Weak prerequisite none
Direct prerequisites – Parallel prerequisite none
Direct prerequisites – Milestone prerequisite none
Direct prerequisites – Exclusion none

Objectives

Programme

PART ONE: CHAOTIC SIGNAL GENERATION BY ANALOG AND SAMPLING PHASE-LOCKED LOOPS

Lecturer: dr. Géza Kolumbán, BME

1.1 Basis concepts

  • goals of chaotic signal generations
  • operation of APLL and SPLL circuits
  • development of baseband models

1.2 Chaotic behavior of APLL and SPLL circuits

  • SPLL: one-dimensional bifurcation diagram
  • APLL: two-dimensional bifurcation diagram
  • properties of generated chaotic signal
  • stability of chaotic attractors

1.3 Laboratory experiment

  • circuit diagram and operation of chaotic APLL
  • design of a chaotic APLL
  • performance evaluation of generated chaotic signals by measurements

PART TWO: BASIC CONCEPTS OF NONLINEAR DYNAMICS AND CHAOS

Lecturer: Dr. Michael Peter Kennedy, UCD

2.1 Dynamical systems

  • basic definitions
  • classification of dynamical systems
  • continuous- and discrete-time dynamical systems
  • existence and uniqueness of solution
  • the flow
  • examples

2.2 Steady-state solutions of dynamical systems

  • wondering and nonwondering states
  • limit points and limit sets
  • attracting limit sets, attractors and basins of attraction
  • equilibrium points and fixed points
  • periodic, quasi-periodic and chaotic steady-state
  • properties of chaotic attractors
  • dimension of attracting limit sets
  • classifications of attractors

2.3 Stability of steady-state solutions

  • stability of equilibrium points
  • eigenvalues, eigenvectors and eigenspaces
  • manifolds
  • homoclinic and heteroclinic orbits
  • Poincaré map
  • chaos in the sense of Shil'nikov
  • Shil'nikov's theorem
  • Lyapunov exponents
  • classification of attracting limit sets

2.4 Structural stability and bifurcations

  • basic definitions
  • Hopf, saddle-node and period-doubling bifurcations
  • routes to chaos: period-doubling, intermittency and torus breakdown
  • bifurcation diagrams
  • parameter space diagram

PART THREE: APPLICATION OF CHAOTIC SIGNALS IN DATA TRANSMISSION

Lecturer: dr. Géza Kolumbán, BME

3.1 Bases of digital communications

  • channel model
  • performance measures
  • orthonormal basis functions and M-ary modulation schemes
  • coherent and noncoherent receivers
  • role of synchronization

3.2 Wideband data communications

  • advantages of and typical applications for wideband data communications
  • conventional approaches
  • usage of chaotic carriers

3.3 Solutions to chaotic communications

  • chaotic modulation techniques
  • multilevel modulation using one or more chaotic basis functions
  • CSK: demodulation by means of synchronization
  • implementation of chaotic synchronization
  • COOK, DCSK and FM-DCSK: demodulation without synchronization

3.4 Performance evaluation of chaotic communications systems

  • performance measures of chaotic communications systems
  • development of low-frequency equivalent model
  • stationarity of chaotic signals
  • effect of symbol duration
  • performance evaluation of CSK, COOK, DCSK and FM-DCSK transceivers

3.5 Noise and interference suppression

  • noise and interference suppression by optimization
  • design of cost function
  • application of noise and interference suppression to the DCSK modulation scheme

3.6 Chaotic WLAN data communications systems

  • survey of WLAN data communications systems
  • development of the INSPECT WLAN FM–DCSK system
  • performance evaluation
The study of nonlinear dynamics and chaotic behavior of electrical systems was started about ten years ago. Understanding of these phenomena explains many strange behaviors of electrical systems which cannot be predicted using the conventional theorems and design approaches. Moreover, the chaotic signals that are "noise-like" signals generated by a known deterministic system have many potential applications from measurement engineering to data transmission. The main goal of this lecture is to discuss the nonlinear dynamics and chaotic behavior of electrical systems in detail and to survey the most important analysis tools applied in this field. The latest results in the field of chaotic communications are also presented. It will be shown that how the knowledge of chaotic signal generator can be exploited for noise and interference suppression. A chaotic wireless local area network WLAN being developed in the framework of the Esprit #31103 INSPECT EU Project will be discussed in detail. As an example the chaotic behavior of sampling and analog phase-locked loop is investigated and the behavior of a chaotic analog PLL is tested by laboratory measurements.

Learning outcomes

Ez a tantárgy a KKK rendeletben meghatározott, következő kompetenciák fejlesztését szolgálja:

Knowledge

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Skills

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Autonomy and responsibility

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Oktatási módszertan

Előadás

Tanulástámogató anyagok

Not provided.

Recommended preliminary knowledge for completing the subject

Knowledge type competencies
(azon előzetes ismeretek összessége, amelyek megléte nem kötelező, de a tantárgy eredményes teljesítését nagyban elősegíti)
Alapfokú nemlineáris hálózatelméleti ismeretek.
Skill type competencies
(azon előzetes képességek és készségek összessége, amelyek megléte nem kötelező, de a tantárgy eredményes teljesítését nagyban elősegíti)
nincs
Recommended (non-compulsory) preliminary competencies
(azon ajánlott (nem kötelező) előzetesen megszerzendő kompetenciák összessége, amelyek jelentősen hozzájárulnak a tantárgy eredményes teljesítéséhez)
Alapfokú nemlineáris hálózatelméleti ismeretek.
General rules
Követelmények: a. A szorgalmi időszakban: mérési feladat sikeres elvégzése b. A vizsgaidőszakban: szóbeli vizsga c. Elővizsga: a szorgalmi időszak utolsó hetében
Assessment methods
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Exam-period assessments

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Grade calculation

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Attendance requirements

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Rules for retake and resubmission

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Short description

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Detailed description

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Recommended courses

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Workload to complete the subject

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