A Useful Chaotic Family with Single Linearity and Circuit Implementation Based on FPGA

Recently, a series of typical three-dimensional dissipative chaotic flows where all but one of the nonlinearities are quadratic are studied. Based on this research, a novel chaotic model with only one single linearity is proposed by introducing cubic terms and four new chaotic systems with various characteristics are found. Besides, a chaotic family with a single linearity is constructed with those four chaotic systems and 12 existing systems SL1-SL12 of the chaotic flows. Exploiting the new systems, basic dynamic behaviors are analyzed, including the strange attractors, equilibrium points, Lyapunov exponents as well as the property of multistability. In addition, the corresponding simulation results are illustrated to show those properties expressly. In realizing the chaotic circuit, we utilize the field programmable gate array (FPGA), which is of considerable flexibility, good programmability and stability, instead of analog devices that are easily affected by surroundings. More importantly, the circuit of the proposed chaotic family is realized on a single FPGA over register transfer level (RTL) using 32-bit fixed-point operation. Finally, an experimental FPGA-based circuit is constructed, and the output results are shown on oscilloscope, which agree well with the numerical simulations.