Any position for Ms or direct PhD?

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Robert May & James Yorke (1970s)
These mathematicians mathematized the topic. Yorke co-wrote the original paper "Period Three Implies Chaos" that gave the field its popular name. Robert May applied these models of chaos to ecology, showing how animal populations can boom and bust in unpredictable

Realized that systems transition into chaos through a series of period-doubling bifurcations,with universal
Mathematical parameters (now known as Feigenbaum Constants) governing them.His studies proved that chaos is governed by universal laws,which govern seemingly unrelated phenomena across nature

Geometric form, proving random complexity could be generated from simple, repetitive rules.
The Universalist: Mitchell Feigenbaum (1970s)
This physicist discovered that the process of going from order to disorder was not random. By studying everything from fluid flow to electronic circuits, he ..

3-Benoît Mandelbrot (1970s)
He asked a simple question: "How long is the coast of Britain?" The answer, he found, will be determined by how long your ruler is. This led him to the discovery of Fractals—endlessly intricate patterns repeating themselves at all scales. He gave chaos its beautiful..

That little error directed him to a massive conclusion: some systems have a Sensitive Dependence on Initial Conditions. He coined this term poetically: The Butterfly Effect sking himself if a butterfly flapping its wings in Brazil would produce a tornado in Texas.

A meteorologist running weather simulations on a primitive machine. He eventually reran a simulation from the midpoint, approximating a figure from 0.506127 to 0.506. The weather forecast turned out to be completely different.

Its starting position that its behavior over the long term would be uncalculably unpredictable. He planted the seed that would grow into deterministic chaos.

2. The Accidental Father: Edward Lorenz (1960s)

Henri Poincaré (Late 1800s)
This French mathematician, long before the term was even invented, arrived at the fundamental idea by mistake. Trying to calculate the "Three-Body Problem" of physics, he found that even a system governed by strict Newtonian laws could be so sensitive to