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A novel Lorenz-type system of nonlinear differential equations is proposed. Unlike the original Lorenz system, where the chaotic dynamics remain confined to the positive half-space with respect to the Z state variable due to a limiting threshold effect, the proposed system enables bipolar swing of this state variable. In addition, the classical set of parameters (a, b, c) controlling the behavior of the Lorenz system are reduced to a single parameter, namely a. Two possible modes of operation are admitted by the system; switching between these two modes results in the creation of a complex butterfly chaotic attractor. Numerical simulations and results from an experimental setup are presented. Index Terms--Chaos, chaotic oscillators, Lorenz system.

In this letter, we show that the two-region third-order piecewise-linear dynamics of the chaotic Colpitts oscillator may be mapped to a Chua's oscillator with an asymmetric nonlinearity.

The topological resemblance of the Colpitts oscillator to that of Chua's circuit suggests that the two circuits may also be similar in their dynamic behavior. The similarity in the dynamics is demonstrated in the present communication by resorting to computer simulation. We deal in particular with the unknown chaotic behavior of the Colpitts oscillator. It is shown by referring to recently published articles that the Colpitts oscillator and Chua's circuit are in fact topologically conjugate one to another.