When Two Dual Chaotic Systems Shake Hands

which is chaotic on a particular parameter set, (σ, ρ, β) = (10, 28, 8/3)1 in the real parameter space of the general system (1); but for other parameter sets, system (1) may not be chaotic. The chaotic Lorenz system (2) has received sustained research interest in the literature since its discovery. For example, in [Tucker, 1999; Stewart, 2000], a rigorous proof confirms the existence of the chaotic attractor in system (2); in [Franceschini et al., 1993], the chaotic attractor of system (2) is characterized in terms of unstable periodic orbits; in [Gilmore et al., 2003, 2007; Mindlin et al., 1990;