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Simplest dissipative chaotic flow. (English) Zbl 1043.37504

Summary: Numerical examination of third-order, autonomous ODEs with one dependent variable and quadratic nonlinearities has uncovered what appears to be the algebraically simplest example of a dissipative chaotic flow. This system exhibits a period-doubling route to chaos for \(2.017<A<2.082\) and is approximately described by a one-dimensional quadratic map.

MSC:

37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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