An equation for continuous chaos. (English) Zbl 1371.37062

Summary: A prototype equation to the Lorenz model of turbulence contains just one (second-order) nonlinearity in one variable. The flow in state space allows for a “folded” Poincaré map (horseshoe map). Many more natural and artificial systems are governed by this type of equation.


37D45 Strange attractors, chaotic dynamics of systems with hyperbolic behavior
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[1] Lorenz, E. N., J. Atmos. Sci., 20, 130 (1963)
[2] Haken, H., Phys. Lett., 53A, 77 (1975)
[3] Samle, S., Bull. Amer. Math. Soc., 73, 747 (1967)
[4] Rössler, O. E., Z. Naturforsch., 31a, 259 (1976)
[5] Li, T. Y.; Yorke, J. A., Amer. Math. Monthly, 82, 985 (1975)
[6] Ruelle, D.; Takens, F., Comm. Math. Phys., 20, 167 (1971) · Zbl 0227.76084
[8] May, R. M., Nature, 256, 165 (1975), London
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