Multicavity formations and complexity modulation in a hyperchaotic discrete system

This paper introduces a novel and unified approach for controlling the directions and number of cavities of a two dimensional Sine ICMIC modulation map (2D-SIMM). Two controllers are added to the system for arranging the cavity fluctuations and translating the cavities respectively. Both the controllers can effectively redesign the dynamics of reproducing cavities in different directions with grid representations. The dynamics of the proposed controlled model are investigated with bifurcation, Lyapunov and FuzzyEn algorithms under various cavity formations in different directions. A relationship is established for the complexity of the phase space with the directional control and various arrangements of the sinusoidal cavities. The proposed model is overall hyperchaotic with the high complexity in the whole parameter plane. The proposed scheme is effective for a dynamical model to reproduce the self phase structure in various arrangements for the optimization and modulation of complexity.