A chaotic map with two-dimensional offset boosting.

A chaotic map with two-dimensional offset boosting is exhaustively studied, which is derived from the Lozi map and shows the controllability of amplitude control. The mechanism of two-dimensional offset boosting is revealed based on the cancelation of offset-involved feedback terms. Furthermore, the coexistence of homogeneous multistability and heterogeneous multistability is disclosed when the offset boosting turns to the initial condition. It is also found that the independent constant term rescales the amplitude of all the sequences without changing the Lyapunov exponents. More strikingly, the parameters for amplitude control and offset boosting are bound together introducing hybrid control. The circuit implementation based on the microcontroller unit is used to validate the theoretical analysis and numerical simulations. This chaotic map is applied for particle swarm optimization showing its stronger performance and robustness in solving optimization problems.