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Coupled oscillator systems with nonlinear characteristics have shown some interesting phenomena and brought improvement to natural science and fundamental research. It is known that two oscillators coupled with an inductor excite two different modes: In-phase single-mode and anti-phase single-mode coexist for some range of parameter values. Both of negative resistors within these oscillators are normal. Such an oscillator is called a soft oscillator or one with soft nonlinearity. In comparison with soft oscillator, hard oscillator has a nonlinear negative resistor whose i v characteristics contain both negative and positive. The characteristics near the origin act as a positive resistor. Therefore the oscillator converges on the origin for small initial values. Greater initial values than the origin stable regions are required to generate the oscillation. Such an oscillator is called hard oscillator or one with hard nonlinearities. Two oscillators with hard nonlinearities coupled with an inductor excite four different modes: Zero (non-oscillation), in-phase single-mode, anti-phase single-mode and double-mode coexist for some range of parameter values [1]. The double-mode shows simultaneous asynchronous oscillations with in-phase and anti-phase frequency components. In particular, the double-mode oscillations are stably excited although they do not occur in the case of common negative resistors with soft nonlinearities. On the basis of this study, we have proposed two coupled chaotic circuits with hard nonlinearities for the purpose of looking for the interesting phenomena as double-mode chaotic oscillations [2][3]. We have confirmed doublemode chaos with one-periodic in-phase and chaotic antiphase single-modes [2] and that with torus and chaos [3], respectively. However, we have not found that with chaos and chaos in these systems. We are considering the reason that phenomena do not exist could be caused by their single circuit architecture. Bifurcation phenomena to chaos depend on the circuit architecture. In this study, we propose two chaotic circuits with hard nonlinearities coupled with an inductor and look for the expected double-mode chaos. Especially, we have adopted a different type of single circuit from the previous studies [2][3].

Double-mode Chaos with Hard Nonlinearities Coupled with an Inductor