A simple second order differential equation, ovals and chaos

mAnasa-taraMgiNI

In our youth as a consequence of our undying fascination with ovals we explored many means of generating them. In course of those explorations we experimentally arrived at a simple second order differential equation that generated oval patterns. It also taught us lessons on chaotic systems emerging from differential equations even before we actually explored the famous Lorenz and Rossler attractors for ourselves. The inspiration came from the very well-known harmonic oscillator which is one of the first differential equations you might study as a layperson: $latex tfrac{d^2x}{dt^2}=-ax$, where $latex a$ is a positive constant that has some direct meaning in physics as the ratio of the restoration constant to the mass of the oscillator. With this foundation, we wondered what might happen if we used a cubic term instead which was in turn coupled to a periodic forcing from a regular harmonic oscillator. Thus, we arrived at the below…

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sudhasarathi61

It is absolutely clear that this world and its contents are purely mental and nothing solid in it. To come out of suffering entirely you should know your mind thoroughly.

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