Linearization of the Lorenz system

• A partial and complete piecewise linearized version of the Lorenz system are addressed.
• The linearized versions have an independent total amplitude control parameter.
• A piecewise linear version of the diffusionless Lorenz system is derived by further linearization.
• A corresponding chaotic circuit without any multiplier is implemented for the chaotic oscillation.

A partial and complete piecewise linearized version of the Lorenz system is proposed. The linearized versions have an independent total amplitude control parameter. Additional further linearization leads naturally to a piecewise linear version of the diffusionless Lorenz system. A chaotic circuit with a single amplitude controller is then implemented using a new switch element, producing a chaotic oscillation that agrees with the numerical calculation for the piecewise linear diffusionless Lorenz system.