Abstract

Chaos and related phenomena in a simple autonomous circuit family consisting of a resistor, inductor, capacitor, negative resistance, and one hysteresis resistor are investigated. All the circuits in this family are described by an n-dimensional canonical piecewise-linear equation containing one small parameter epsilon . In the case where epsilon is small enough, the analysis is simplified into the hysteretic connecting n-1-dimensional linear system. Therefore, a sufficient condition of chaos generation is rigorously derived for n=3, and an interesting transition from torus to chaos is verified for n=4. >

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