In this paper, a new digital chaos circuit which can generate multiple-scroll strange attractors is proposed. Being based on the piecewise-linear function which is determined by on-chip supervised learning, the proposed digital chaos circuit can generate multiple-scroll strange attractors. Hence, the proposed circuit can exhibit various bifurcation phenomena. By numerical simulations, the learning dynamics and the quasi-chaos generation of the proposed digital chaos circuit are analyzed in detail. Furthermore, as a design example of the integrated digital chaos circuit, the proposed circuit realizing the nonlinear function with five breakpoints is implemented onto the FPGA (Field Programmable Gate Array). The synthesized FPGA circuit which can generate n-scroll strange attractors (n=1, 2, 4) showed that the proposed circuit is implementable onto a single FPGA except for the SRAM.

In this paper, an FPGA (Field Programmable Gate Array)-implementable digital chaos circuit with nonlinear mapping function learning ablility is proposed. The features of this circuit are user-programmability of the mapping functions by on-chip supervised learning, robustness of chaos signal generation based on digital processing, and high-speed and low-cost thanks to its FPGA implementation. The circuit design and analysis are presented in detail. The learning dynamics of the circuit and the quantitization effect to the quasi-chaos generation are analyzed by numerical simulations. The proposed circuit is designed by using an FPGA CAD tool, Verilog-HDL. This confirmed that the one-dimensional chaos circuit block (except for SRAM's) is implementable on a single FPGA chip and can generate quasi-chaos signals in real time.

A new current-mode sampled-data chaos circuit is proposed. The proposed circuit is composed of an operation block, a parameter block, and a delay block. The nonlinear mapping functions of this circuit are generated in the neuro-fuzzy based operation block. And these functions are determined by supervised learning. For the proposed circut, the dynamics of the learning and the state of the chaos are analyzed by computer simulations. The design conditions concerning the bifurcation diagram and the nonlinear mapping function are presented to clarify the chaos generating conditions and the effect of nonidealities of the proposed circuit. The simulation results showed that the nonlinear mapping functions can be realized with the precision of the order of several percent and that different kinds of bifurcation modes can be generated easily.