Isomorphic transformation of the Lorenz equations into a single-control-parameter structure

Abstract An isomorphic structure that converts the Lorenz equations, whose dynamic properties are usually described in terms of three independent factors, into a single control-parameter system, is put forward and analyzed. Such an isomorphism is shown to bring an intrinsic simplification that offers much better depictions of the Lorenz non-linear dynamics, while it allows for quicker and forthright inspection of the control-parameter domains, inside which well-defined periodic, both symmetric and asymmetric, as well as chaotic solutions occur.

Keywords Lorenz equations, Fluid turbulence, Laser theory, Instabilities and chaos, Nonlinear dynamics

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Dynamic analyses of a flat plate and a beam subjected to a moving load

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