Introducing Undergraduate Electrical Engineering Students to Chaotic Dynamics: Computer
Simulations with Logistic Map and Buck Converter
Sajid IqbalPh.D studentHarbin Institute of Technology
Contents
• Determinism• Nonlinear Dynamics: bifurcations and chaos• Introducing nonlinear dynamics in Undergraduate
Electrical Engineering• Simulation results Logistic map DC-DC buck converter
Laplace described determinism as, “If you give methe positions and momenta of all the particles in theUniverse, I will predict all past and future.”
Bifurcation is a sudden qualitative change in the behavior of a dynamical system caused by the variation of its parameters.
“We collectively wish to apologize for havingmisled the general educated public by spreadingideas about the determinism of systems satisfyingNewtons’ laws of motion that, after 1960, wereproved to be incorrect.”
Sir James Lighthill collectiveapology on behalf of allscientists
Deterministic Chaos is an unstable aperiodicbehavior in deterministic dynamical system, whichshows sensitive dependence on initial conditions.
Edward Lorenz coined the term ‘Butterfly Effect’.
The advent of chaos theory shattered and obscuredthe well-regarded Newtonian vision.
The consequence of chaos is that complexbehavior need not have complex causes.
The logistic map also known as the “Verhulst model” is given as
Xn +1 = k * Xn (1-Xn) 0 < k < 4
Where parameter ‘k’ represents the population growth rate and ‘Xn’ is the variable at the nth iteration.
A time series plot is a display of data points thatshows how values have changed over uniform timeintervals.
A bifurcation diagram is a visual summary chart ofthe behaviors exhibited by a dynamical system,when some parameters are varied.
Logistic map simulation results (cont.)
The iterated solutions reappear everysecond value
Period-2 orbit
2n nv v+ =
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