Nonlinear Dynamical Systems Analysis

Another research presentation that I gave for juniors. Topics below were presented via simulations on Mathematica notebooks.

• Dynamic simulations for dynamical systems which are nonlinear in nature will be presented. Systems include Driven Damped Harmonic Oscillator and Solitons emerging from the KdV equation.

• Driven Damped Harmonic Oscillator Phase Space analysis will be shown via dynamic real time simulations of the system in addition to Amplitude vs frequency plot as it changes with quality factor showing how resonance is achieved for particular values of the driving frequency.

• The Korteweg-de Vries Equation (KdV equation) describes the theory of water waves in shallow channels, such as a canal. It is a non-linear equation which exhibits special solutions, known as solitons, which are stable and do not disperse with time. Furthermore there are solutions with more than one soliton which can move towards each other, interact and then emerge at the same speed with no change in shape (but with a time “lag” or “speed up”)- this led them to being called as waves behaving as particles.

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