Limit sets | Nonlinear systems | Dynamical systems

Limit cycle

In mathematics, in the study of dynamical systems with two-dimensional phase space, a limit cycle is a closed trajectory in phase space having the property that at least one other trajectory spirals into it either as time approaches infinity or as time approaches negative infinity. Such behavior is exhibited in some nonlinear systems. Limit cycles have been used to model the behavior of a great many real-world oscillatory systems. The study of limit cycles was initiated by Henri Poincaré (1854–1912). (Wikipedia).

Limit cycle
Video thumbnail

Computing Limits from a Graph with Infinities

In this video I do an example of computing limits from a graph with infinities.

From playlist Limits

Video thumbnail

3 The limit laws

Describing the common laws of limits. Knowing these will greatly simplify your calculations of limits.

From playlist Life Science Math: Limits in calculus

Video thumbnail

1A Introduction to this course on limits

A course on limits in calculus for healthcare and life sciences students.

From playlist Life Science Math: Limits in calculus

Video thumbnail

2.2 The Limit of a Function

OpenStax Calculus Volume 1

From playlist Calculus 1

Video thumbnail

The Limit Does NOT Exist (Limit Example 4)

Epsilon Definition of a Limit In this video, I illustrate the epsilon-N definition of a limit by showing that the limit of (-1)^n as n goes to infinity does NOT exist. The method I present is more generally useful to show that a limit does not exist. Other examples of limits can be seen

From playlist Sequences

Video thumbnail

Limit doesn't exist 2 variables example

Example of how to show a limit doesn't exist for a function of 2 variables.

From playlist Engineering Mathematics

Video thumbnail

Limits of a Sequence

The video introduces the concept of determining if sequence converges or diverges. http://mathispower4u.yolasite.com/

From playlist Limits

Video thumbnail

Determining Limits

http://mathispower4u.wordpress.com/

From playlist Limits

Video thumbnail

Part 1: Formal Definition of a Limit

This video states the formal definition of a limit and provide an epsilon delta proof that a limit exists. complete Video Library at http://www.mathispower4u.com

From playlist Limits

Video thumbnail

2/21, Patrick Speissegger

Patrick Speissegger, McMaster University A new Hardy field of relevance to Hilbert's 16th problem In our paper, we construct a Hardy field that embeds, via a map representing asymptotic expansion, into the field of transseries as described by Aschenbrenner, van den Dries and van der Hoev

From playlist Spring 2020 Kolchin Seminar in Differential Algebra

Video thumbnail

Neural oscillations, weak coupling and networks by Bard Ermentrout

Dynamics of Complex Systems - 2017 DATES: 10 May 2017 to 08 July 2017 VENUE: Madhava Lecture Hall, ICTS Bangalore This Summer Program on Dynamics of Complex Systems is second in the series. The theme for the program this year is Mathematical Biology. Over the past decades, the focus o

From playlist Dynamics of Complex Systems - 2017

Video thumbnail

Lecture 11 | MIT 6.832 Underactuated Robotics, Spring 2009

Lecture 11: Walking Instructor: Russell Tedrake See the complete course at: http://ocw.mit.edu/6-832s09 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 6.832 Underactuated Robotics, Spring 2009

Video thumbnail

Lec 32 | MIT 18.03 Differential Equations, Spring 2006

Limit Cycles: Existence and Non-existence Criteria. View the complete course: http://ocw.mit.edu/18-03S06 License: Creative Commons BY-NC-SA More information at http://ocw.mit.edu/terms More courses at http://ocw.mit.edu

From playlist MIT 18.03SC Differential Equations, Fall 2011

Video thumbnail

MAE5790-13 Hopf bifurcations in aeroelastic instabilities and chemical oscillators

Supercritical vs subcritical Hopf. Airplane wing vibrations. Flutter. Chemical oscillations. Computer simulations. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 8.2, 8.3.

From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

Video thumbnail

J. Smillie - Horocycle dynamics (Part 2)

A major challenge in dynamics on moduli spaces is to understand the behavior of the horocycle flow. We will motivate this problem and discuss what is known and what is not known about it, focusing on the genus 2 case. Specific topics to be covered include: * SL_2(R) orbit closures and inva

From playlist Ecole d'été 2018 - Teichmüller dynamics, mapping class groups and applications

Video thumbnail

Lai-Sang Young: A mathematical Theory of Strange Attractors

This lecture was held at The University of Oslo, May 24, 2006 and was part of the Abel Prize Lectures in connection with the Abel Prize Week celebrations. Program for the Abel Lectures 2006 1. “A Scandinavian Chapter in Analysis” by Lennart Carleson, Kungliga Tekniska Högskolan, Swed

From playlist Abel Lectures

Video thumbnail

MAE5790-10 van der Pol oscillator

Origins of the van der Pol oscillator in radio engineering. Strongly nonlinear limit. Liénard transformation. Relaxation oscillations. Weakly nonlinear limit. Energy method for estimating the amplitude of the limit cycle. Reading: Strogatz, "Nonlinear Dynamics and Chaos", Sections 7.4--7.

From playlist Nonlinear Dynamics and Chaos - Steven Strogatz, Cornell University

Video thumbnail

Theory of synchronization - CEB T2 2017 - Pikovsky - 1/3

Arkady Pikovsky (Univ. Potsdam) - 18/04/17 Theory of synchronization 1) Basics - oscillators, phase and amplitudes - isochrons and phase response curve - phase dynamics under small forcing - phase locking and frequency entrainment - beyond phase approximation - effects of noise -

From playlist 2017 - T2 - Stochastic Dynamics out of Equilibrium - CEB Trimester

Video thumbnail

Mathematical Biology. 21: Hopf Bifurcations

UCI Math 113B: Intro to Mathematical Modeling in Biology (Fall 2014) Lec 21. Intro to Mathematical Modeling in Biology: Hopf Bifurcations View the complete course: http://ocw.uci.edu/courses/math_113b_intro_to_mathematical_modeling_in_biology.html Instructor: German A. Enciso, Ph.D. Text

From playlist Math 113B: Mathematical Biology

Video thumbnail

Limit Points

Limit Points In this video, I define the notion of a limit point (also known as a subsequential limit) and give some examples of limit points. Limit points are closed: https://youtu.be/b1jYloJXDYY Check out my Sequences Playlist: https://www.youtube.com/playlist?list=PLJb1qAQIrmmCuFxFs

From playlist Sequences

Related pages

Periodic point | Limit set | Self-oscillation | Attractor | Jordan curve theorem | Phase space | Hilbert's sixteenth problem | Action potential | Stationary point | Mathematics | Stable manifold | Hyperbolic set | Henri Poincaré | Bendixson–Dulac theorem | Orbit (dynamics) | Van der Pol oscillator | Image (mathematics) | Poincaré–Bendixson theorem | Hodgkin–Huxley model