On Bifurcations from A Four Dimensional Hysteresis Circuit Family

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  • 4次元ヒステリシス回路族の分岐現象について

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Abstract

This article discusses a four dimensional autonomous circuit family that includes one hysteresis element. The circuit family is governed by two symmetric three dimensional linear equations connected to each other by hysteresis switchings. We transform the equation into Jordan form and derive theoretical formulae of the two dimensional return map, its Jacobian matrix and its Jacobian and show the following novel results: (1) Classification of the phenomena by evaluation of Lyapunov exponents using the formulae, (2) Period doubling route to chaos and the transition to hyperchaos via crisis, (3) Basic bifurcation of these phenomena, (4) Implementation example and laboratory measurements of some attractors.

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