Abstract
Within the discipline of applied mathematics, a large part of dynamical systems theory is concerned with the description of the qualitative behavior of dynamical systems.
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It is possible to show that differential equations must have at least a three-dimensional state variable to show chaos. This is because a trajectory cannot intersect itself; in two dimensions you either proceed to a fixed point or end up on a limit cycle.
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Ramsay, J., Hooker, G. (2017). Qualitative Behavior. In: Dynamic Data Analysis. Springer Series in Statistics. Springer, New York, NY. https://doi.org/10.1007/978-1-4939-7190-9_6
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DOI: https://doi.org/10.1007/978-1-4939-7190-9_6
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