Two-variable boosting bifurcation in a hyperchaotic map and its hardware implementation

Abstract

There are few reports on the nondestructive adjustment of the oscillation amplitude of the chaotic sequence in the discrete map. To study the lossless regulation of the oscillation amplitude of chaotic sequences, this article proposes a new simple two-dimensional (2D) hyperchaotic map with trigonometric functions. It not only exhibits the offset boosting bifurcation and offset boosting coexistence attractors, but also shows the offset boosting of two state variables with respect to arbitrary parameters in the 2D map. The simulation results of bifurcation diagram, maximum Lyapunov exponent and attractor phase diagram show that the map can produce complex dynamical behaviors. In addition, the introduction of new control parameters into the 2D hyperchaotic map can also make the hyperchaotic map exhibit rich multi-stable phenomena. At the same time, the covariation of the initial state and control parameters can result in arbitrary switching and coexistence of attractors in the phase plane. The 2D hyperchaotic map was tested and verified by hardware experiment platform. Moreover, we design a pseudo-random number generator (PRNG) to test the hyperchaotic map. The results show that the pseudo-random numbers generated by the hyperchaotic map have high randomness.