This paper discusses a four-dimensional plus hysteresis autonomous chaotic circuit. The circuit dynamics are described by two symmetric four-dimensional linear equations connected to each other by hysteresis switchings. We transform the equation into Jordan form and derive theoretical formulas of its three-dimensional return map, its Jacobian matrix and its Jacobian. These formulas can be developed easily to general dimensional cases and are used to evaluate Lyapunov exponents. Also we have discovered a torus doubling route to chaos and then to hyperchaos. Some of the return map attractors are confirmed by laboratory experiments. A rough two parameters bifurcation diagram is also given.
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