The Lü system is a particular case of the Lorenz system

Abstract Between the so-called Lorenz-like systems, the Lu system, x ˙ = a ( y − x ) , y ˙ = c y − x z , z ˙ = − b z + x y , has attracted great interest in the last decade. In this Letter we show that, generically ( c ≠ 0 ), there is a homothetic transformation which converts the Lu system into the Lorenz system and, therefore, all the dynamical behavior exhibited by the Lu system is also present in the Lorenz system. Consequently, all the results obtained in the papers devoted to the study of the Lu system can be trivially derived from the corresponding results on the Lorenz system.

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