For a certain set of parameters the system exhibits chaotic behavior and forms what is called a strange attractor.
From the en.wikipedia.org
For example, the Ruelle-Takens scenario describes how a periodic orbit bifurcates into a torus and the torus into a strange attractor.
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David Ruelle and Floris Takens later predicted, against Landau, that fluid turbulence could develop through a strange attractor, a main concept of chaos theory.
From the en.wikipedia.org
Since the beginning of chaos theory when Edward Lorenz accidentally discovered a strange attractor with his computer, computers have become an indispensable source of information.