Synchronization of PWL function-based 2D and 3D multi-scroll chaotic systems

We study the synchronization of a piecewise linear function-based chaotic system. That system generates multiple scrolls in multiple directions (two- and three-directions) on phase space. In this scenario, the design of a controller based on Generalized Hamiltonian forms is possible. As function of control signals, we propose a master-slave synchronization scheme using 2 (n) -1 combinations to drive a nonlinear state observer. Associated with this, the piecewise linear functions of the slave are directly controlled by the state-variables of the master system. We computed the synchronization error for each combinations. Besides, the circuit synthesis based on operational amplifiers validates our synchronization scheme by means of SPICE simulations. We observed that the synchronization error at circuit level depends on the number of the control signals used. Our numerical and SPICE simulation results are in agreement showing the usefulness of the proposed approach.