A hyperchaotic map with grid sinusoidal cavity. (January 2018) - Yu, Mengyao; Sun, Kehui; Liu, Wenhao; He, Shaobo
Highlights: An approach for constructing high-dimensional chaotic map is introduced. Based on the closed-loop modulation coupling pattern, a new sinusoidal cavity hyperchaotic system (SCS) is firstly proposed. The SCS is extended as grid sinusoidal cavity system (GSCS) by combining coupling control and piecewise-linear controller. The directions and number of cavities can be controlled. The GSCS shows complicated dynamical behaviors, high complexity and uniform distribution. So it has good application prospect in image encryption. Abstract: Based on closed-loop modulation coupling pattern and the model of sinusoidal cavity, a high-dimensional sinusoidal cavity hyperchaotic system is proposed. The number of sinusoidal cavities is controlled by the system parameters. By designing a piecewise-linear controller, the grid sinusoidal cavity attractors are obtained. The equilibrium points are theoretically analyzed through mathematical calculation. Taking the two-dimensional grid sinusoidal cavity hyperchaotic map as an example, dynamics of the system are analyzed by phase diagram, equilibrium points, Lyapunov exponents spectrum, bifurcation diagram, complexity and distribution characteristics. The results show that it has rich dynamical behaviors, including complicated phase space trajectory, hyperchaotic behavior, large maximum Lyapunov exponent and typical bifurcations. The proposed hyperchaotic map has advantages in complexity and distribution in the whole parameter space. Therefore, it has good application prospects in secure communication.