This paper introduces the first fully digital implementation of a 3rd order ODE-based chaotic oscillator with signum nonlinearity. A threshold bus width of 12-bits for reliable chaotic behavior is observed, below which the system output becomes periodic. Beyond this threshold, the maximum Lyapunov exponent (MLE) is shown to improve up to a peak value at 16-bits and subsequently decrease with increasing bus width. The MLE is also shown to gradually increase with number of introduced internal delay cycles until a peak value at 14 cycles, after which the system loses chaotic properties. Introduced external delay cycles are shown to rotate the attractors in 3-D phase space. Bus width and delay elements can be independently modulated to optimize the system to suit specifications. The experimental results of the system show low area and high performance on a Xilinx Virtex 4 FPGA with throughput of 13.35 Gbits/s for a 32-bit implementation. © 2011 IEEE.
Mansingka A.S., Radwan A.G., Zidan M.A., Salama K.N.
32-bit implementation; Chaotic behaviors; Chaotic oscillators; Chaotic properties; Delay cycle; Delay elements; Digital implementation; Low area; Maximum Lyapunov exponent; Non-Linearity; Peak values; Phase spaces; System output; Busbars; Buses; Circuit oscillations; Delay circuits; Digital circuits; Electric network analysis; Lyapunov methods; Phase space methods; Chaotic systems
Midwest Symposium on Circuits and Systems, Art. No. 6026596, Doi: 10.1109/MWSCAS.2011.6026596