Dynamics of multicavity hyperchaotic maps with rotational control operation and its applications

Abstract

Abstract To provide more complex and random chaotic maps to applications and algorithms, we propose a boundary coupled modulation (BCM) model. By introducing the rotation-matrix (ROT), the corresponding rotation boundary coupled modulation (RBCM) model are constructed, and a series of hyperchaotic maps are generated with various attractors and numerous fixed points. The shape and size of the multicavity can be adjusted by controlling the parameters. Interestingly, RBCM maps are controlled by changing rotation coefficients (Rot-C, d, e, and θ), which can rotate the attractor of the enhanced BCM at any angle and direction. RBCM maps produce a more uniform topological space, and have multiple pairs of symmetric coexisting attractors. The BCM and RBCM maps exhibit rich dynamical behaviors, high complexity, and strong randomness.To verify the engineering practicability, we apply the BCM and RBCM maps to design pseudo-random number generators (PRNG), and test it with NIST, quadrature amplitude modulation (QAM) system. Finally, the FPGA implementation of the proposed chaotic map verifies.