The peculiar features of the memristor, a fundamental passive two-terminal element characterized by nonlinear relationship between charge and flux, promise to revolutionize integrated circuit design in the next few decades. Besides its most popular potential applications, ultra-dense non-volatile memories and brain-simulating systems, much research has been lately devoted to their use in chaotic circuits. Although the physical memristor is inherently-asymmetric, complementary behaviors arise in devices with opposite polarity. In this work we demonstrate that this makes it feasible to devise a number of practical realizations of a monotone-increasing odd-symmetric charge-flux nonlinearity suitable for chaos-based applications through the sole use of physical memristors of the kind recently fabricated at Hewlett-Packard Labs. Confirmation for such claim is obtained through comparison of chaotic behavior of two modified Chua's oscillators, in which the nonlinear diode is replaced in one case with an artificial memristor with symmetric nonlinearity and in the other case with one of the proposed symmetric memristor combinations
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