Author Archives: cybersuneel

Lectures on Chaos, Fractals and Dynamical Systems

Posted on May 18, 2011 by cybersuneel

National Programme on Technology Enhanced Learning (NPTEL) has a course titled Chaos, Fractals and Dynamical Systems.  The lectures of the course are available in video format here.  The speaker is Prof. Soumitro Banerjee of the Electrical Engineering Department, IIT Kharagpur.

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Butterfly Effect

Posted on May 13, 2011 by cybersuneel

The term butterfly effect has gained social relevance and acceptance in recent years.  The movie The Butterfly Effect and its sequels are a case in point.  The term generally refers to a seemingly insignificant change in circumstances leading to a … Continue reading →

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Sensitivity to Initial Conditions (SIC)

Posted on May 8, 2011 by cybersuneel

In this post, we visit a phenomenon characteristic to all chaotic systems: sensitivity to initial conditions (SIC). Let a system be started with two different initial conditions, say, and .  If the difference between and is small in magnitude, then … Continue reading →

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Stair-Step Diagram

Posted on May 2, 2011 by cybersuneel

In the previous post, we had a look at the bifurcation diagram – a very useful tool in studying nonlinear systems.  In this post, we have a look at another useful tool in understanding the dynamics of nonlinear maps – … Continue reading →

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Logistic Map – Bifurcation Diagram

Posted on April 27, 2011 by cybersuneel

In the last post, we studied the dynamics of the logistic map , by looking at the plots of a few of its trajectories for various values of the bifurcation parameter .  In this post, we try to get a … Continue reading →

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Logistic Map

Posted on April 25, 2011 by cybersuneel

Introduction This blog is about chaos and nonlinear phenomena.  The prototype example of chaotic dynamics has always been the one-dimensional difference equation called the logistic map.  In this post, let us have a first look at this interesting equation.

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