Fractals, Chaos and Dynamical Systems Team
Team Mentor: Dr. Dipendra Sengupta
Team Members
Donald Charity, Freshman/Math Major
Cory Ellis, Junior/Applied Math Major
Brian Jordan, Senior/Applied Math Major
Donald Charity, Freshman/Math Major
Tammara Ward, Junior/Math Major
Lakisha Mundon, Sophomore/Math Major
Ayonda Moore, Junior/Math Major
Abstract
Most naturally occuring processes are inherently nonlinear and
can give rise to very complex behaviors. Even very simple mathematical models
can exhibit behavior that give rise to extremely convoluted (and often very
beautiful) fractal shapes. The discovery of this fundamentally new area of
mathematics has been crucially dependent on computational intensive graphic
methods and has given birth to a radically new paradigm for mathematical
research: experimental research.
In this project we will perform experimental mathematical investigation.
The mathematical contents will comprise fractals, nonlinear dynamics and
mathematical chaos.
We will study the orbits of a family of quadratic dynamical systems and
investigate the period doubling route to chaos. We will design and develop
mathematical materials and Mathematica programs necessary to do the
investigation.
We will apply fundamental mathematical concepts to a wide variety of
physical, biological and social processes (e.g., population growth, measles
problem, growth of plant, problems of epidemiology, and the economics of arms
race). The deep connection between geometry and nonlinear dynmaics will be
explored and computer programs will be developed to generate fractal maps and
pictures of compelling beauty. Finally, through guided work in experimental
mathematics students will acquire a deeper understanding of mathematical and
scientific thinking.
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Brian Jordan, Ayonda Moore, and Donald Charity prepare for the SOARS '96
Conference.
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Dr. Sengupta assists Brian Jordan with a problem.
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