Attractor Merging and Amplitude Control of Hyperchaos in a Self-Reproducing Memristive Map

Abstract

Memristor-type feedback provides a unique passage for chaos produced with easy control. In this work, a novel memristive map with amplitude control and coexisting hyperchaotic attractors is designed, in which two nonbifurcation parameters are extracted for partial amplitude control crossing the origin and total amplitude control. Attractor splitting and attractor merging are captured, which lead to five regimes of attractor self-reproducing. In this case, double-cavity attractors extend in the direction of 0${}^{\circ }$, 45${}^{\circ }$, 90${}^{\circ }$ in negative $x$-axis, 90${}^{\circ }$ in positive $x$-axis, 135${}^{\circ }$ in $x$-axis forming a specific wall of self-reproduction. Furthermore, the FPGA-based hardware implementation is carried out showing consistent results with numerical simulation. Finally, a high-security chaotic encryption scheme is proposed for the orthogonal frequency division multiplexing transmission system, where the power division multiplexing technique and two-dimensional region joint encryption are effectively utilized. The security of the transmitted information is improved by the various coexisting attractors and nonbifurcation amplitude controllers.