Dynamics, FPGA realization and application of a chaotic system with an infinite number of equilibrium points

Abstract

Recently, systems with infinite equilibria have attracted interest because they can be considered as systems with hidden attractors. In this work, we introduce a new elegant system with an open curve of equilibrium points. It has just one parameter (a) and an exponential function. We show the dynamics of such a new chaotic oscillator by computing the Lyapunov exponents’ spectrum and bifurcation diagram, and it is implemented by using a field-programmable gate array (FPGA). The exponential function is approached by power series and then implemented with adders and multipliers within the FPGA. Experimental results are provided for the attractor as well as for the synchronization of two chaotic oscillators to transmit an image, thus demonstrating the usefulness of the new oscillator in a chaotic secure communication system.