Persistence of Chaos in Coupled Lorenz Systems Mehmet Onur Fen Basic Sciences Unit, TED University, 06420 Ankara, Turkey E-mail: monur.fen@gmail.com, Tel: +90 312 585 0217 The dynamics of unidirectionally coupled chaotic Lorenz systems is investigated. It is revealed that chaos is present in the response system regardless of generalized synchronization. The presence of sensitivity is theoretically proved, and the auxiliary system approach and conditional Lyapunov exponents are utilized to demonstrate the absence of synchronization. Periodic motions embedded in the chaotic attractor of the response system is demonstrated by taking advantage of a period-doubling cascade of the drive. The obtained results may shed light on the global unpredictability of the weather dynamics and can be useful for investigations concerning coupled Lorenz lasers. Keywords: Lorenz system; Persistence of chaos; Sensitivity; Period-doubling cascade; Generalized synchronization Chaos theory, whose foundations were laid by Poincaré [1], has attracted a great deal of attention beginning with the studies of Lorenz [2, 3]. A mathematical model consisting of a system of three ordinary differential equations were introduced by Lorenz [3] in order to investigate the dynamics of the atmosphere. This model is a simplification of the one derived by Saltzman [4] which originate from the Rayleigh-Bénard convection. The demonstration of sensitivity in the Lorenz system can be considered as a milestone in the theory of dynamical systems. Nowadays, this property is considered as the main ingredient of chaos [5]. A remarkable behavior of coupled chaotic systems is the synchronization [6]-[10]. This concept was studied for identical systems in [9] and was generalized to non-identical systems by Rulkov et al. [10]. Generalized synchronization (GS) is characterized by the existence of a transformation from the trajec- tories of the drive to the trajectories of the response. A necessary and sufficient condition concerning the asymptotic stability of the response system for the presence of GS was mentioned in [11], and some numerical techniques were developed in the papers [10, 12] for its detection. Even though coupled chaotic systems exhibiting GS have been widely investigated in the literature, the presence of chaos in the dynamics of the response system is still questionable in the absence of GS. arXiv:1610.02218v1 [nlin.CD] 7 Oct 2016 1 1 Introduction Abstract